## Powers

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.

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7^{0}=1, 3^{0}=1, 12^{0}=1,
x^{0}=1

Remember also that

###
7 = 7^{1}, 3= 3^{1}, etc.

### Multiplying and Dividing Numbers with Indices

If I can state a couple of rules by example

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7^{3} × 7^{2}= 7^{(3+2)}= 7^{5}

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7^{5} ÷ 7^{2}= 7^{(5-2)}
= 7^{3}

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

###
7^{3} × 7^{2}= (7 × 7× 7) × (7× 7) =7^{5}

and
###
7^{5} ÷ 7^{2}= (7 × 7× 7× 7× 7) ÷ (7× 7)
= 7^{3}

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

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