# 10.1.5 Negative Exponents

## Activity: Further Investigation of Exponents

Work out the “long way” and using the rules for powers with the same base.

The rule gives , so means .

We read as “10 to the power negative four.” [ You learned about reciprocals in Unit 7 when dividing fractions. ] Often, the word “power” is left out and we say “10 to the negative four” instead. In the same way, is said as “five to the negative two” and means , or , which is equivalent to .

Alternatively, you can say that is the reciprocal of .

## Activity: Understanding Negative Powers

Without using your calculator, write the following numbers as fractions or whole numbers, as appropriate.

(a)

(a)

(b)

(b)

(c)

### Comment

What does any number to the power 0 equal?

(c)

(d)

(d)

## Activity: Writing Negative Numbers

Write the following as powers of 10.

(a) 0.01

### Comment

Convert the number to a fraction first, thinking back to place value if you need to.