Answer
$512$
Work Step by Step
In this problem, we can break big numbers down to be able to work with them with more ease.
$32$ can be broken down to base $2$ raised to the $5th$ power whereas $256$ can be broken down to $2$ raised to the $8th$ power:
$2^{5} \cdot (2^{8})^{\frac{1}{2}}$
Raising a power to a power means we can multiply the two exponents together, keeping the same base.
Multiply the exponents together first:
$2^{5} \cdot 2^{\frac{8}{2}}$
Reduce the fraction in the exponent by dividing both numerator and denominator by $2$, the greatest common factor:
$2^{5} \cdot 2^{4}$
To multiply exponents that have the same base, we just add the exponents together and keep the same base:
$2^{9}$
Evaluate by raising $2$ to the power of $9$:
$512$
