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

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

Simplify the expression.

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

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

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

Cancel the common factor of $2$ .

Factor $2$ out of $4$ .

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

Cancel the common factor.

$16^{2 \frac{1}{2 \cdot 2}}$

Rewrite the expression.

$16^{\frac{1}{2}}$

Rewrite $16$ as $4^{2}$ .

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

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

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

Cancel the common factor of $2$ .

Cancel the common factor.

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

Rewrite the expression.

$4^{1}$

Evaluate the exponent.

$4$