Question

What makes the statement true? 9^-2=?

(Can someone help explaining step by step?)

Answer 1

9^-2 can be written as 1/9^2 which is 1/81

Answer 2

You need to simplify using the laws of indices.

Recall that,


`{a}^( - m) = \frac{1}{ {a}^(m) }`

We apply this property to obtain,


`{9}^( - 2) = \frac{1}{ {9}^(2) }`

Recall again that,


`{a}^(2) = a * a`

Therefore our expression become,


`{9}^( - 2) = (1)/( 9 * 9 )`

This gives us,


`{9}^( - 2) = (1)/( 81 )`

You should also take note of this property too.

`{a}^( m) = \frac{1}{ {a}^(-m) }`