Evaluate Using the Given Value f(1/2)=36^(1/2)

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

Step 1

Simplify the expression.

Rewrite $36$ as $6^{2}$ .

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

Apply the power rule and multiply exponents, ${(a^{m})}^{n} = a^{m n}$ .

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

Step 2

Cancel the common factor of $2$ .

Cancel the common factor.

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

Rewrite the expression.

$f (\frac{1}{2}) = 6$