Simplify (2x^(-1/4)y^(3/4))^4

${(2 x^{- \frac{1}{4}} y^{\frac{3}{4}})}^{4}$

Step 1

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

${(2 \frac{1}{x^{\frac{1}{4}}} y^{\frac{3}{4}})}^{4}$

Step 2

Combine $2$ and $\frac{1}{x^{\frac{1}{4}}}$ .

${(\frac{2}{x^{\frac{1}{4}}} y^{\frac{3}{4}})}^{4}$

Step 3

Combine $\frac{2}{x^{\frac{1}{4}}}$ and $y^{\frac{3}{4}}$ .

${(\frac{2 y^{\frac{3}{4}}}{x^{\frac{1}{4}}})}^{4}$

Step 4

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

Apply the product rule to $\frac{2 y^{\frac{3}{4}}}{x^{\frac{1}{4}}}$ .

$\frac{{(2 y^{\frac{3}{4}})}^{4}}{{(x^{\frac{1}{4}})}^{4}}$

Apply the product rule to $2 y^{\frac{3}{4}}$ .

$\frac{2^{4} {(y^{\frac{3}{4}})}^{4}}{{(x^{\frac{1}{4}})}^{4}}$

Step 5

Simplify the numerator.

Raise $2$ to the power of $4$ .

$\frac{16 {(y^{\frac{3}{4}})}^{4}}{{(x^{\frac{1}{4}})}^{4}}$

Multiply the exponents in ${(y^{\frac{3}{4}})}^{4}$ .

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

$\frac{16 y^{\frac{3}{4} \cdot 4}}{{(x^{\frac{1}{4}})}^{4}}$

Cancel the common factor of $4$ .

Cancel the common factor.

$\frac{16 y^{\frac{3}{4} \cdot 4}}{{(x^{\frac{1}{4}})}^{4}}$

Rewrite the expression.

$\frac{16 y^{3}}{{(x^{\frac{1}{4}})}^{4}}$

Step 6

Simplify the denominator.

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

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

$\frac{16 y^{3}}{x^{\frac{1}{4} \cdot 4}}$

Cancel the common factor of $4$ .

Cancel the common factor.

$\frac{16 y^{3}}{x^{\frac{1}{4} \cdot 4}}$

Rewrite the expression.

$\frac{16 y^{3}}{x^{1}}$

Simplify.

$\frac{16 y^{3}}{x}$