Simplify (256x^16)^(1/4)

${(256 x^{16})}^{\frac{1}{4}}$

Step 1

Simplify the expression.

Apply the product rule to $256 x^{16}$ .

$256^{\frac{1}{4}} {(x^{16})}^{\frac{1}{4}}$

Rewrite $256$ as $4^{4}$ .

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

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

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

Step 2

Cancel the common factor of $4$ .

Cancel the common factor.

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

Rewrite the expression.

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

Step 3

Simplify the expression.

Evaluate the exponent.

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

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

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

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

Cancel the common factor of $4$ .

Factor $4$ out of $16$ .

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

Cancel the common factor.

$4 x^{4 \cdot 4 \frac{1}{4}}$

Rewrite the expression.

$4 x^{4}$