Question

Which expression is equivalent to 36^-1/2

Answer 1

ANSWER


$( {36})^{ (- \frac{1}{2}) } = \frac{1}{6}$


EXPLANATION



The given expression is


${36}^{( - \frac{1}{2} )}$
This is having a negative index. We must first of all change to a positive index.


Recall that,



${a}^{ - m} = \frac{1}{ {a}^{m} }$

We apply this law of exponents to get,



${36}^{( - \frac{1}{2} )} = \frac{1}{ {36}^{( \frac{1}{2} )} }$

We cab rewrite the given expression to obtain;



${36}^{( - \frac{1}{2} )} = \frac{1}{ \sqrt{36} }$

This will simplify to give us,


${36}^{( - \frac{1}{2} )} = \frac{1}{ 6 }$

Answer 2

$36^{- \frac{1}{2} }= \cfrac{1}{36^{ \frac{1}{2} }} = \cfrac{1}{(6^2)^{ \frac{1}{2} }} = \cfrac{1}{6}$