Pass Check: Indices & Powers

Apply the laws of indices, including negative, fractional and zero powers.

4 definitions3 to memorise3 common mistakes5 exam questions8-question quiz

Index/power/exponent

The small number showing how many times a base is multiplied by itself, e.g. in 3⁴, 4 is the index.

Base

The number being raised to a power, e.g. in 3⁴, 3 is the base.

Reciprocal power

A negative index means one over the base to the positive power: a^-n = 1/a^n.

Fractional power

a^(1/n) means the nth root of a; a^(m/n) means the nth root of a, then raised to the power m.

Quick check

Mixed quiz

1. Evaluate 3^-2.

2. Which value of n satisfies 2^n = 1/32?

3. Simplify 4^5 x 4^2, giving your answer as a single power.

4. Evaluate 5^-2.

5. Evaluate 4^-2.

6. Which is equivalent to 9^(3/2)?

7. Which is equal to 4⁻¹?

8. Evaluate 2^-2.