Evaluate (4^16)^(1/2)

${(4^{16})}^{\frac{1}{2}}$

Step 1

Multiply the exponents in ${(4^{16})}^{\frac{1}{2}}$ .

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

$4^{16 (\frac{1}{2})}$

Cancel the common factor of $2$ .

Factor $2$ out of $16$ .

$4^{2 (8) \frac{1}{2}}$

Cancel the common factor.

$4^{2 \cdot 8 \frac{1}{2}}$

Rewrite the expression.

$4^{8}$

Step 2

Raise $4$ to the power of $8$ .

$65536$