Edexcel IGCSE

Powers and roots

An index is shorthand for repeated multiplication, and a root runs that shorthand backwards. This is section 1.4 of the Edexcel International GCSE Mathematics A specification, and it bundles four things that look separate on a syllabus but share one engine: the index laws, writing a number as a product of powers of its prime factors, finding an HCF or an LCM, and — Higher tier only — surds and fractional powers. The engine is counting. An index counts how many copies of the base are multiplied together, so multiplying two powers pushes the counts together and dividing takes one away from the other. Get the counting right and the arithmetic follows.

Edexcel IGCSE 4MA142 approved practice questions

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Before you start

What you need to be able to do already

If any of these is shaky, fix it first — every worked example below leans on all three.

List the factors and the multiples of a whole number, and say whether a number is prime
Write down every factor of $36$ . There are nine of them: $1, 2, 3, 4, 6, 9, 12, 18, 36$ , and a missed one is how an HCF answer goes wrong. If that list came slowly, fix this first — the HCF question below is this list set beside the factors of $48$ with the largest shared number circled, and prime factorisation is the same skill run with primes only.
Simplify a fraction, and turn one upside down to write its reciprocalFractions
Write down the reciprocal of $\frac{2}{5}$ , then work out $\frac{1}{3 ^{2}}$ . They are $\frac{5}{2}$ and $\frac{1}{9}$ . Every negative index on this page becomes a fraction the moment you use it: $3^{- 1} = \frac{1}{3}$ and $3^{- 2} = \frac{1}{9}$ , so if fractions are shaky the negative-index questions will be too.
Read decimal place value, and swap a terminating decimal for the fraction it equalsDecimals
Write $0.375$ as a fraction in its simplest form. It is $\frac{3}{8}$ . Two things here need it: $9^{0.5}$ and $9^{\frac{1}{2}}$ are the same instruction, and a power of a decimal is read straight off the calculator — $1.0 3^{4} = 1.12550881$ , which you then have to give to the accuracy the question named.

The idea

What is powers and roots?

In $a^{n}$ , the bottom number $a$ is the base and the small raised number $n$ is the index: it says how many copies of the base are multiplied together, so $5^{4} = 5 \times 5 \times 5 \times 5 = 625$ . A root is the same statement read backwards — $364 = 4$ because $4^{3} = 64$ . Everything else in this section is built out of those two readings. Prime factorisation writes a number as powers of primes, an HCF and an LCM can be read straight off two such factorisations, and a surd is simply a root that has no exact decimal, so it is left written as a root.

The notation, and how to read it

Every worked solution below is written in these five symbols.

SymbolReads asMeans
$a^{n}$ $a$ to the power $n$ $n$ copies of $a$ multiplied together. $a$ is the base, $n$ is the index. The index laws change only the index — the base is carried through untouched.
$a^{0}$ $a$ to the power zeroExactly $1$ , for any base except $0$ . It is not $0$ , and it is not $a$ . $\frac{a ^{n}}{a ^{n}}$ is $a^{n - n} = a^{0}$ and is also plainly $1$ , so the two must agree.
$a^{- n}$ $a$ to the power minus $n$ The reciprocal, $\frac{1}{a ^{n}}$ . The minus sign flips the number over, it does not make it negative: $3^{- 2} = \frac{1}{9}$ , never $- 9$ .
$a^{m / n}$ $a$ to the power $m$ over $n$ Take the $n$ th root, then raise to the power $m$ : $8^{2/3} = (38)^{2} = 2^{2} = 4$ . The bottom of the fraction is the root, the top is the power. Higher tier.
$n a$ the $n$ th root of $a$ The number that gives $a$ when raised to the power $n$ . With no small number written, it is the square root: $64 = 8$ , while $364 = 4$ .

The one idea underneath all of it

An index is a count, so every index law is just arithmetic on counts — and it only works when the two powers share the same base. Multiplying puts the counts side by side, so you add them. Dividing cancels one count against the other, so you subtract. A bracket raised to a power repeats the whole count, so you multiply. Reading the laws this way also settles the three cases that look like exceptions rather than making you memorise them: $a^{0} = 1$ because dividing a power by itself leaves nothing, $a^{- n}$ is a reciprocal because carrying on dividing past zero keeps dividing, and $a^{\frac{1}{2}}$ is a square root because $a^{\frac{1}{2}} \times a^{\frac{1}{2}} = a^{1}$ and only the square root does that.

The smallest possible example

$5^{4} \div 5^{2}$ , with both powers written out in full.

$5^{4} \div 5^{2} = 5^{4 - 2} = 5^{2} = 25$

$5^{4}$ is $5 \times 5 \times 5 \times 5$ and $5^{2}$ is $5 \times 5$ . Dividing cancels two of the fives, and two are left. That is all 'subtract the indices' ever means — it is a count of what survives the cancelling, not a rule to remember. Notice what did not happen: the base stayed $5$ . It did not become $25$ , and $4 \div 2$ was never worked out. Every index law on this page is this same picture.

Key terms

The words a question will use

Exam wording is precise. These five carry the meaning a question depends on.

TermWhat it meansNotation
Index (plural: indices)
The small raised number that counts the copies of the base. 'Power' and 'exponent' are the same thing under different names, and exam papers use all three, so treat 'the index laws', 'the laws of indices' and 'the power rules' as one topic. $5^{4}$
Product of prime factors
A number rewritten as primes multiplied together, with any repeats collected up as powers. The stem asks for it 'as a product of powers of its prime factors', and $2 \times 2 \times 3 \times 5$ is not that answer until the repeat is written as $2^{2}$ . $2^{2} \times 3 \times 5$
Highest common factor (HCF)
The largest number that divides into both numbers exactly. It cannot be bigger than the smaller of the two, which is the fastest way to reject a wrong answer: $24$ divides $48$ but not $36$ , so it can never be the HCF of $36$ and $48$ . $HCF (36, 48) = 12$
Lowest common multiple (LCM)
The smallest number both numbers divide into exactly. Multiplying the two together always gives a common multiple, but usually not the lowest one — $6 \times 8 = 48$ is a genuine common multiple of $6$ and $8$ , and it is still the wrong answer, because $24$ gets there first. $LCM (6, 8) = 24$
Surd
An irrational number written exactly using a root sign, such as $3$ . Higher tier only. 'Give your answer in surd form' means the root sign stays in the answer; a rounded calculator decimal is only an approximation and does not answer that instruction. $75 = 53$

The method

How to work out a powers and roots

Five steps, in this order. The worked examples below point back to these numbers.

Check the powers share the same base, and write that base down.The index laws only apply to powers of one and the same number. In $5^{4} \div 5^{2}$ the base is $5$ throughout, so they apply. In $2^{3} \times 3^{2}$ they do not, and there is nothing to do but work both out. Writing the base down first is also what stops the recorded mistake of changing it: $u^{7} \times u^{- 3}$ keeps the base $u$ , it does not turn into $2 u^{4}$ , and $5^{4} \div 5^{2}$ is not $2 5^{2}$ .
Clear any brackets first: a power raised to a power multiplies the two indices. $(6^{4})^{5} = 6^{4 \times 5} = 6^{20}$ , because twenty copies is five lots of four copies. A negative index goes through the same multiplication: $(6^{- 3})^{2} = 6^{(- 3) \times 2} = 6^{- 6}$ . Brackets come first here for exactly the reason they come first everywhere else. The recorded error on this step is adding rather than multiplying — $(3^{2})^{3}$ is $3^{6}$ , not $3^{5}$ — and it is the difference between $729$ and $243$ .
For a multiplication of two powers of that base, add the indices. $3^{4} \times 3^{2} = 3^{4 + 2} = 3^{6}$ , because four copies next to two copies is six copies. Add them as signed numbers, not as sizes: $3^{5} \times 3^{- 2} = 3^{5 + (- 2)} = 3^{3}$ , and $5 + (- 2)$ is $3$ . Treating the minus sign as though it were not there is the recorded mistake here — it is the student who writes $7 + (- 3) = 10$ when the answer is $4$ . Add the indices, never multiply them, and never touch the bases.
For a division, subtract the bottom index from the top one, in that order. $\frac{3 ^{6}}{3 ^{5}} = 3^{6 - 5} = 3^{1}$ . Both the order and the sign are load-bearing, and both are recorded mistakes here. Backwards: $\frac{3 ^{3}}{3 ^{4}}$ is $3^{3 - 4} = 3^{- 1}$ , not $3^{1}$ . Sign dropped: $\frac{6 ^{23}}{6 ^{- 6}}$ is $6^{23 - (- 6)} = 6^{29}$ , not $6^{17}$ , because subtracting a negative adds. Write the subtraction out with its brackets before you evaluate it.
Read what the index now says, then answer in the form the question named.A positive index means work it out: $5^{2} = 25$ . Zero means $1$ , never $0$ . A negative index means the reciprocal, not a negative answer: $3^{- 1} = \frac{1}{3}$ , and $3^{- 2} = \frac{1}{9}$ , not $- 9$ . A fractional index means root first, then power: $8^{\frac{2}{3}} = (38)^{2} = 4$ . Then match the form. 'Give your answer as an integer' wants $25$ written out; 'in the form $3^{n}$ ' wants $3^{- 1}$ left exactly as it stands, and evaluating it to $0.333 \dots$ throws the accuracy mark away.

Use it when

The expression is built from powers of one and the same base, combined by $\times$ , $\div$ , or a bracket raised to a power: $5^{4} \div 5^{2}$ , $\frac{3 ^{4} \times 3 ^{2}}{3 ^{5}}$ , $\frac{3 ^{5} \times 3 ^{- 2}}{3 ^{4}}$ , $\frac{6 ^{3} \times ( 6 ^{4} ) ^{5}}{( 6 ^{- 3} ) ^{2}}$ . Once you have spotted the common base, the whole question is arithmetic on the indices and the base just comes along for the ride.

Do not use it when

There is no common base, or the question belongs to one of the other strands of this section. $2^{3} \times 3^{2}$ has no shared base, so work each power out and multiply: $8 \times 9 = 72$ . Powers that are added or subtracted have no law at all — $3^{2} + 3^{3}$ is $9 + 27 = 36$ , and there is nothing to combine. Writing an integer as a product of powers of its prime factors is repeated division by the smallest prime that fits ( $60 \to 30 \to 15 \to 5$ , giving $2^{2} \times 3 \times 5$ ); multiply your answer back out and check you land on the number you started with, because the wrong answers offered alongside it come to $180$ , $120$ and $30$ . An HCF or an LCM is found by listing factors or multiples, or by comparing two prime factorisations. And a surd is simplified by pulling out the largest square factor: $75 = 25 \times 3 = 53$ . Roots do not split over a sum — $9 + 16$ is $25 = 5$ , not $3 + 4$ — and surds only add when the number under the root already matches, so $5 + 5 = 25$ while $2 + 3$ simply stays as it is.

Worked examples

6 IGCSE Maths practice questions on powers and roots, fully worked

One per objective, so the range is covered rather than the same question repeated. Every step is written out, and the answer is shown — this is study material, not a test.

Example 1

Work out which of these numbers is a square number. [1 mark]

Identify square numbers and cube numbers

Worked solution

Step 1: A square number is the result of multiplying a whole number by itself.
Step 2: Check each option: $8 \times 8 = 64$ , so 64 is a square number.
Step 3: For the other options: 50 is not a square, 72 is not a square, 99 is not a square.

Answer64

Example 2

Work out the value of 5 squared plus the cube root of 64. [2 marks]

Calculate squares, square roots, cubes and cube roots

Worked solution

Step 1: First, calculate 5 squared: 5 squared means $5 \times 5 = 25$ .
Step 2: Next, find the cube root of 64: we need a number that when multiplied by itself three times gives $64.4 \times 4 \times 4 = 64$ , so the cube root is 4.
Step 3: Now add the two results together: $25 + 4 = 29$ .

Answer29

Example 3

Work out $5^{4} \div 5^{2}$ . Give your answer as an integer. [1 mark]

Use index notation and index laws for multiplication and division of positive and negative integer powers including zero

Worked solution

Step 1: Identify the base: both terms have base 5.
Step 2: For division with the same base, subtract the exponents: $4 - 2 = 2$ .
Step 3: So the expression simplifies to 5².
Step 4: Calculate 5² = $5 \times 5 = 25$ .

Answer25

Show 3 more worked examples

Example 4

Write 60 as a product of powers of its prime factors. [2 marks]

Express integers as a product of powers of prime factors

Worked solution

Step 1: Start by dividing 60 by the smallest prime number, 2: $60 \div 2 = 30$ .
Step 2: 30 is still even, divide by 2 again: $30 \div 2 = 15$ .
Step 3: 15 is not even, so try the next prime: $15 \div 3 = 5$ .
Step 4: 5 is a prime number itself, so stop.
Step 5: Collect the factors: $60 = 2 \times 2 \times 3 \times 5 = 2$ ² × $3 \times 5$ .

Answer2² ×

3 \times 5

Example 5

Work out the lowest common multiple (LCM) of 6 and 8. [1 mark]

Find highest common factors (HCF) and lowest common multiples (LCM)

Worked solution

Step 1: List the first few multiples of 6: 6, 12, 18, 24, 30, 36, 42, 48, .
Step 2: List the first few multiples of 8: 8, 16, 24, 32, 40, 48, .
Step 3: Find the smallest multiple that appears in both lists.
Step 4: The smallest common multiple is 24.

Answer24

Example 6

Which of the following is a surd? [1 mark]

Understand the meaning of surds

Worked solution

Step 1: A surd is a square root that cannot be simplified to a whole number.
Step 2: Check $25$ : $25 = 5 \times 5$ , so $25 = 5$ , a whole number — not a surd.
Step 3: Check $8$ : $8 = 4 \times 2$ and $4 = 2$ , but 2 cannot be removed, so $8$ is irrational — it is a surd.
Step 4: Check $49$ and $100$ : both are perfect squares, so they simplify to whole numbers — not surds.

Answer

8

Common mistakes

Where marks actually get lost

Learnly tags 14 distinct misconceptions on this subtopic. These are errors that show up in real student work — not generic revision advice.

Examiner traps

Adding exponents incorrectly
What goes wrong: Students add exponents when multiplying powers with the same base, but forget to handle negative signs correctly, e.g., thinking 7 + (-3) = 10 instead of 4.
What to do instead: When multiplying powers with the same base, add the exponents. For positive and negative numbers, remember: 7 + (-3) = 4.
Subtracting exponents incorrectly
What goes wrong: Students subtract exponents in the wrong order when dividing, e.g., for u^7 / u^{-3}, they might do $7 - 3 = 4$ instead of 7 - (-3) = 10.
What to do instead: When dividing powers with the same base, subtract the exponent of the denominator from the numerator. For u^7 / u^{-3}, do 7 - (-3) = 10.
Zero power equals zero
What goes wrong: Students think any number to the power of zero equals zero, instead of one.
What to do instead: Any non-zero number raised to the power of zero equals 1. For example, u^ $0 = 1$ , not 0.
Negative power makes negative base
What goes wrong: Students think a negative exponent turns the base negative, e.g., u^{-3} = -u^3 instead of 1/u^3.
What to do instead: A negative exponent means reciprocal, not negative. u^{-3} = 1 / u^3, not -u^3.
Multiplying bases with exponents
What goes wrong: Students multiply the bases when multiplying powers with the same base, e.g., u^7 * u^{-3} = u^{ $7 - 3$ } = u^4 but they might write 2u^4 incorrectly.
What to do instead: When multiplying powers with the same base, keep the base and add the exponents. Do not multiply the bases.
Multiply denominator only
What goes wrong: When rationalising the denominator, students multiply only the denominator by the surd, forgetting to multiply the numerator as well.
What to do instead: Remember: to rationalise, multiply both numerator and denominator by the same surd, like multiplying by 1.

See 8 more examiner traps

Confuse surd with square root
What goes wrong: Students think √a × √a = a√a instead of a, or incorrectly simplify surds like √ $20 = 2$ √10.
What to do instead: √a × √a = a, not a√a. Simplify surds by finding square factors: √20 = √ $(4 \times 5) = 2$ √5.
Add surds incorrectly
What goes wrong: Students add surds by adding the numbers inside the root, e.g., √5 + √5 = √10, or √2 + √3 = √5.
What to do instead: Only add surds with the same radicand: √5 + √ $5 = 2$ √5. √2 + √3 cannot be simplified.
Rationalise with wrong surd
What goes wrong: When rationalising a denominator like 1/(√ $5 + 2$ ), students multiply by √5 instead of √ $5 - 2$ .
What to do instead: For a denominator like √a + b, multiply numerator and denominator by √a - b (the conjugate).
Adding exponents when multiplying
What goes wrong: Students incorrectly add exponents when multiplying powers with the same base, e.g., 3² × 3³ = 3⁵ (correct) but they might think it's 3⁶ by adding $2 + 3 + 1$ ? Actually the error is more subtle: they might add exponents when they should multiply, but the main error is confusing multiplication and addition rules.
What to do instead: When multiplying powers with the same base, ADD the exponents. For example, 3² × 3³ = 3^ $(2 + 3) = 3$ ⁵. Do not multiply the exponents.
Flipping base instead of reciprocal
What goes wrong: Students think a negative exponent means the base becomes negative, e.g., 3⁻² = -3², rather than taking the reciprocal.
What to do instead: A negative exponent means take the reciprocal of the base and then apply the positive exponent. For example, 3⁻² = 1/(3²) = $\frac{1}{9}$ , not -9.
Reversing root and power order
What goes wrong: Students apply the root and power in the wrong order for fractional exponents, e.g., 8^( $\frac{2}{3}) = (8$ ²)^ $(\frac{1}{3})$ is correct but they might do 8^( $\frac{2}{3}) = (8$ ^ $(\frac{1}{3})$ )²? Actually both are correct, but the error is doing the root after squaring incorrectly, or thinking 8^( $\frac{2}{3}) = (8$ ²)/3.
What to do instead: For a fractional exponent like a^(m/n), first take the n-th root of a, then raise to the power m. Or do the power first then root. For example, 8^ $(\frac{2}{3})$ = (∛8)² = 2² = 4.
Subtracting exponents in wrong order
What goes wrong: When dividing powers, students subtract the exponents in the wrong order, e.g., 3⁵ ÷ 3² = 3^ $(5 - 2)$ is correct, but they might do 3^ $(2 - 5) = 3$ ⁻³.
What to do instead: When dividing powers with the same base, subtract the exponent of the denominator from the exponent of the numerator. For example, 3⁵ ÷ 3² = 3^ $(5 - 2) = 3$ ³.
Adding exponents for power of power
What goes wrong: Students add exponents when raising a power to a power, e.g., (3²)³ = 3^ $(2 + 3) = 3$ ⁵ instead of 3^ $(2 \times 3) = 3$ ⁶.
What to do instead: When raising a power to another power, MULTIPLY the exponents. For example, (3²)³ = 3^ $(2 \times 3) = 3$ ⁶. Do not add them.

Exam technique

How the marks are actually awarded

Method marks are given for working a marker can follow. This is what to put on the page.

Where the marks are: Questions on this section run from $1$ to $4$ marks. The one-mark ones are single moves — $5^{4} \div 5^{2}$ , or the LCM of $6$ and $8$ — with no method mark to fall back on, so the answer has to be right first time. From two marks upwards it is the working that carries you, and on this topic the working is one line: write the indices down before you simplify them, $3^{4 + 2 - 5}$ for $\frac{3 ^{4} \times 3 ^{2}}{3 ^{5}}$ , or $3^{5 + (- 2) - 4}$ for $\frac{3 ^{5} \times 3 ^{- 2}}{3 ^{4}}$ . That line survives an arithmetic slip in a way a bare wrong answer does not. The four-mark question in this bank, $\frac{6 ^{3} \times ( 6 ^{4} ) ^{5}}{( 6 ^{- 3} ) ^{2}}$ , expects each law on its own visible line — brackets, then multiplication, then division — rather than one leap to $6^{29}$ , and its worked solution is exactly those four lines. On the Higher-tier surd questions the three marks follow the three moves of the solution: spot the square factor or the conjugate, expand, then give the simplified form.
Command words to expect: Work outCalculateSimplifyFindWrite downWrite as a product of powers of its prime factorsGive your answer as an integerExpress your answer in the form $3^n$Give your answer in simplified surd formYou must show all your working
Accuracy and rounding: Most answers on this section are exact, and the mark is for leaving them exact. 'In the form $3^{n}$ ' means the answer is $3^{- 1}$ , not $0.333$ ; 'as an integer' means $25$ , not $5^{2}$ ; read which one you were asked for. Surd form means the root sign stays, so $33$ is the answer and $5.196$ is not, however accurate it looks. A product of prime factors must have its repeats collected as powers — $2^{2} \times 3 \times 5$ , not $2 \times 2 \times 3 \times 5$ — and an HCF or LCM is always a whole number. Only where a root genuinely has to be evaluated does rounding enter at all, and then it is $3$ significant figures unless the question names something else.
Calculator: A calculator is allowed in every paper of this qualification, on both Foundation and Higher tiers, which makes the power and root keys the useful ones here: $1.0 3^{4} = 1.12550881$ is one keystroke sequence, and $364 = 4$ needs no thought. What it will not do is choose the form of the answer, and on this topic that is where the marks are. Type $75$ into a calculator on a surd question and you get $8.6602540 \dots$ , which is worth nothing; type $\frac{3 ^{5} \times 3 ^{- 2}}{3 ^{4}}$ in and you get $0.333 \dots$ where the paper asked for $3^{- 1}$ . Use it to check the value of an index line you have already written down, not to replace it.

Check yourself

You should now be able to:

Recognise a square number and a cube number, and say why $64$ is both.
Work out squares, cubes, square roots and cube roots, including inside a longer calculation such as $5^{2} + 364$ .
Apply the multiplication and division index laws to positive and negative integer powers of the same base, keeping the base unchanged.
Multiply the indices when a power is raised to a power, and add them when two powers are multiplied, without confusing the two.
Say what $a^{0}$ and $a^{- n}$ mean, and give $3^{- 2}$ as $\frac{1}{9}$ rather than $- 9$ .
Write an integer as a product of powers of its prime factors, collecting repeats as powers and checking by multiplying back.
Find the highest common factor of two numbers, from their factor lists or from their prime factorisations.
Find the lowest common multiple of two numbers, and explain why it is usually not the two numbers multiplied together.
Higher tier: explain what a surd is, and simplify one by taking out its largest square factor.
Higher tier: add, subtract and multiply surds, and rationalise a denominator by multiplying top and bottom by the conjugate.
Higher tier: simplify and evaluate expressions with fractional and negative indices, such as $8^{\frac{2}{3}}$ .

Specification coverage

The 8 things 4MA1 asks you to do

The assessable objectives for numbers and the number system — powers and roots, in the order the specification lists them.

Identify square numbers and cube numbers
Calculate squares, square roots, cubes and cube roots
Use index notation and index laws for multiplication and division of positive and negative integer powers including zero
Express integers as a product of powers of prime factors
Find highest common factors (HCF) and lowest common multiples (LCM)
Understand the meaning of surds

Show 2 more objectives

Manipulate surds, including rationalising a denominator
Use index laws to simplify and evaluate numerical expressions involving integer, fractional and negative powers

See who is stuck on powers and roots before you teach it.

Create a class, share the 8-character code, and set powers and roots as practice. Your students work through all 42 approved practice questions — not just the 6 on this page — and you see which objectives the class has not got yet. Free for individual students and teachers.

How Learnly works for teachers

Set up your class — free Practise on your own

What you need to be able to do already

List the factors and the multiples of a whole number, and say whether a number is prime

Simplify a fraction, and turn one upside down to write its reciprocalFractions

Read decimal place value, and swap a terminating decimal for the fraction it equalsDecimals

What is powers and roots?

The notation, and how to read it

The words a question will use

Index (plural: indices)

Product of prime factors

Highest common factor (HCF)

Lowest common multiple (LCM)

Surd

How to work out a powers and roots

6 IGCSE Maths practice questions on powers and roots, fully worked

Work out which of these numbers is a square number. [1 mark]

Work out the value of 5 squared plus the cube root of 64. [2 marks]

Work out 54÷52 . Give your answer as an integer. [1 mark]

Write 60 as a product of powers of its prime factors. [2 marks]

Work out the lowest common multiple (LCM) of 6 and 8. [1 mark]

Which of the following is a surd? [1 mark]

Where marks actually get lost

Adding exponents incorrectly

Subtracting exponents incorrectly

Zero power equals zero

Negative power makes negative base

Multiplying bases with exponents

Multiply denominator only

Confuse surd with square root

Add surds incorrectly

Rationalise with wrong surd

Adding exponents when multiplying

Flipping base instead of reciprocal

Reversing root and power order

Subtracting exponents in wrong order

Adding exponents for power of power

How the marks are actually awarded

You should now be able to:

The 8 things 4MA1 asks you to do

See who is stuck on powers and roots before you teach it.

Work out $5^{4} \div 5^{2}$ . Give your answer as an integer. [1 mark]