Need to Know

Indices

The rules you must have ready for the exam.

How to use this: say each rule in your head, then tap Show me to check.

The basics

1 rule

Rule 01

What the letters mean

In b^p = n: b is the base, p the power, n the value.

Only combine powers with the same base.

1 rule

Rule 02

The two laws

a^p × a^q = a^p+q

a^p ÷ a^q = a^p−q

1 rule

Rule 03

Two shortcuts

a⁰ = 1 a^−p = 1 / a^p

1 rule

Rule 04

Power of a power

(a^p)^q = a^pq

Brackets: raise everything inside to the power. (3x)² = 9x².

1 rule

Rule 05

Roots as powers

a^½ = √a

So a surd on the bottom becomes a negative/fractional power.

Mathslive.ie · Indices · Need to Know