Recall the multiplication law: a^m × a^n = a^m+n Add the indices: x^2+3 State the answer: x^5 Answer: x^5

Recall the multiplication law: a^m × a^n = a^m+n Add the indices: y^4+5 State the answer: y^9 Answer: y^9

Recall the division law: a^m ÷ a^n = a^m-n Subtract the indices: x^7-3 State the answer: x^4 Answer: x^4

Simplify (y^8)/(y^2).

Recall the division law: a^m ÷ a^n = a^m-n Subtract the indices: y^8-2 State the answer: y^6 Answer: y^6

Recall the power-of-a-power law: (a^m)^n = a^mn Multiply the indices: x^3 × 2 State the answer: x^6 Answer: x^6

Index laws in algebra Worked Solutions — GCSE Maths

Fully worked, step-by-step solutions to GCSE Index laws in algebra questions. See exactly how to solve problems on multiplication law, adding indices, division law, subtracting indices.

multiplication lawadding indicesdivision lawsubtracting indicespower lawmultiplying indices

GCSE Foundation70 questionsStep-by-step solutions

Question 1

1 markeasy

Simplify

x^2 \times x^3

Worked solution

Recall the multiplication law
$a^m \times a^n = a^{m+n}$
When multiplying powers of the same base, keep the base and add the indices.
Add the indices
$x^{2+3}$
The base x stays the same and the indices 2 and 3 are added.
State the answer
$x^{5}$
Two plus three is five, so the answer is x to the power 5.

Answer

x^{5}

Question 2

1 markeasy

Simplify

y^4 \times y^5

Worked solution

Recall the multiplication law
$a^m \times a^n = a^{m+n}$
Multiplying powers of the same base means adding the indices.
Add the indices
$y^{4+5}$
Keep the base y and add 4 and 5.
State the answer
$y^{9}$
Four plus five is nine, so the answer is y to the power 9.

Answer

y^{9}

Question 3

1 markeasy

Simplify

x^7 \div x^3

Worked solution

Recall the division law
$a^m \div a^n = a^{m-n}$
When dividing powers of the same base, subtract the indices.
Subtract the indices
$x^{7-3}$
Keep the base x and subtract 3 from 7.
State the answer
$x^{4}$
Seven minus three is four, so the answer is x to the power 4.

Answer

x^{4}

Question 4

1 markeasy

Simplify

\frac{y^8}{y^2}

Worked solution

Recall the division law
$a^m \div a^n = a^{m-n}$
A fraction of powers with the same base means subtract the indices.
Subtract the indices
$y^{8-2}$
Keep the base y and subtract 2 from 8.
State the answer
$y^{6}$
Eight minus two is six, so the answer is y to the power 6.

Answer

y^{6}

Question 5

1 markeasy

Simplify

(x^3)^2

Worked solution

Recall the power-of-a-power law
$(a^m)^n = a^{mn}$
A power raised to another power means multiply the indices.
Multiply the indices
$x^{3 \times 2}$
Keep the base x and multiply 3 by 2.
State the answer
$x^{6}$
Three times two is six, so the answer is x to the power 6.

Answer

x^{6}

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