Index laws

Apply index laws to multiply and divide terms with the same base, and simplify expressions using the power of a power law.

Worked examples

Multiplying powers with the same base

Straightforward

Problem

Simplify

5^3 \times 5^4

Dividing powers with the same base

Moderate

Problem

Simplify

7^8 \div 7^3

Combining the power of a power and multiplication laws

Challenging

Problem

Simplify

(2^4)^3 \times 2^5

Practise

Q1·Straightforward

Simplify

2^3 \times 2^4

. Write your answer as

2^n

— what is

n

Q2·Straightforward

Simplify

3^2 \times 3^5

. Write your answer as

3^n

— what is

n

Q3·Straightforward

Simplify

5^1 \times 5^3

. Write your answer as

5^n

— what is

n

Q4·Straightforward

Simplify

a^4 \times a^6

. Write your answer as

a^n

— what is

n

Q5·Moderate

Simplify

4^7 \div 4^3

. Write your answer as

4^n

— what is

n

Q6·Moderate

Simplify

6^5 \div 6^2

. Write your answer as

6^n

— what is

n

Q7·Moderate

Simplify

m^9 \div m^4

. Write your answer as

m^n

— what is

n

Q8·Moderate

Simplify

\dfrac{x^{10}}{x^6}

. Write your answer as

x^n

— what is

n

Q9·Challenging

Simplify

(2^3)^4

. Write your answer as

2^n

— what is

n

Q10·Challenging

Simplify

(a^5)^3

. Write your answer as

a^n

— what is

n

Q11·Challenging

Simplify

3^2 \times 3^4 \div 3^3

. Write your answer as

3^n

— what is

n

Q12·Challenging

Simplify

(y^3)^2 \times y^4

. Write your answer as

y^n

— what is

n