Question

What makes the statement true? 9^-2=? (Can someone help explaining step by step?)

Answer 1

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,

${a}^{2} = a \times a$

Therefore our expression become,

${9}^{ - 2} = \frac{1}{ 9 \times 9 }$

This gives us,

${9}^{ - 2} = \frac{1}{ 81 }$

You should also take note of this property too.
${a}^{ m} = \frac{1}{ {a}^{-m} }$


$This means that the sign of the index changes whenever you reciprocate a number that is raised to a given index$

Answer 2

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