GCSE

Start off by going to Key Skills

Introduction

I will just state a few points

any number to the power zero is one, e.g.

7⁰=1,    3⁰=1,    12⁰=1,     x⁰=1    

Remember also that

7 = 7¹,    3= 3¹,    etc.

Multiplying and Dividing Numbers with Indices

If I can state a couple of rules by example

7³ × 7²= 7⁽³⁺²⁾= 7⁵

7⁵ ÷ 7²= 7^(5-2) = 7³

To see how these rules work, consider the 'long method' in each case.

7³ × 7²= (7 × 7× 7) × (7× 7) =7⁵

and

7⁵ ÷ 7²= (7 × 7× 7× 7× 7) ÷ (7× 7) = 7³

These rules can be generalized to more complicated problems, for example

\[ \frac{7^5 \times 7^2}{7^3} \] \[ = \frac{7^7}{7^3} \] \[ =7^4 \]