Simplify the Radical Expression (256x^2y^-16)^(1/4)

${(256 x^{2} y^{- 16})}^{\frac{1}{4}}$

Step 1

Rewrite the expression using the negative exponent rule $b^{- n} = \frac{1}{b^{n}}$ .

${(256 x^{2} \frac{1}{y^{16}})}^{\frac{1}{4}}$

Step 2

Multiply $256 x^{2} \frac{1}{y^{16}}$ .

Combine $256$ and $\frac{1}{y^{16}}$ .

${(x^{2} \frac{256}{y^{16}})}^{\frac{1}{4}}$

Combine $x^{2}$ and $\frac{256}{y^{16}}$ .

${(\frac{x^{2} \cdot 256}{y^{16}})}^{\frac{1}{4}}$

Step 3

Move $256$ to the left of $x^{2}$ .

${(\frac{256 \cdot x^{2}}{y^{16}})}^{\frac{1}{4}}$

Step 4

Use the power rule ${(a b)}^{n} = a^{n} b^{n}$ to distribute the exponent.

Apply the product rule to $\frac{256 x^{2}}{y^{16}}$ .

$\frac{{(256 x^{2})}^{\frac{1}{4}}}{{(y^{16})}^{\frac{1}{4}}}$

Apply the product rule to $256 x^{2}$ .

$\frac{256^{\frac{1}{4}} {(x^{2})}^{\frac{1}{4}}}{{(y^{16})}^{\frac{1}{4}}}$

Step 5

Simplify the numerator.

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

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

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

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

Cancel the common factor of $4$ .

Cancel the common factor.

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

Rewrite the expression.

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

Evaluate the exponent.

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

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

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

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

Cancel the common factor of $2$ .

Factor $2$ out of $4$ .

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

Cancel the common factor.

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

Rewrite the expression.

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

Step 6

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

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

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

Cancel the common factor of $4$ .

Factor $4$ out of $16$ .

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

Cancel the common factor.

$\frac{4 x^{\frac{1}{2}}}{y^{4 \cdot 4 \frac{1}{4}}}$

Rewrite the expression.

$\frac{4 x^{\frac{1}{2}}}{y^{4}}$

Simplify the Radical Expression (256x^2y^-16)^(1/4)

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