Question

find the value of root 3^-2

Answer 1

√3⁻²=√(1/3)²=√1/9=1/3(Ans.)

Answer 2

If you've studied the laws of Indices, then you must know $a^{-1}$ can be writen as $\frac{1}{a}$.

The negative value of exponent becomes positive when transfered to the denominator.

Thus, $3^{-2}$  can be written as $\frac{1}{3^{2} }$.

Root of $\frac{1}{3^{2} }$ = $\sqrt{\frac{1}{9} }$

Square root will give two values i.e. both positive and negative.

or, +$\frac{1}{3}$    or   -$\frac{1}{3}$ [ Ans]