Whether the given expression is true or false. Given information: 9^{

Question

Whether the given expression is true or false.
Given information:

9^{- \frac{1}{2}} = - 3

Answer 1

Concept used:
Reciprocal rule:

a^{- n} = \frac{1}{a^{n}}

Calculation:

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

And 9 is the square of 3.
So we can write it as

9^{- \frac{1}{2}} = \frac{1}{9^{\frac{1}{2}}} = \frac{1}{3^{2 \times \frac{1}{2}}} = \frac{1}{3} \neq - 3

Therefore,

9^{- \frac{1}{2}} \neq - 3

Hence, the given information is false.

Expert Answer