Simplify (16x^16y^-8)^(3/4)

${(16 x^{16} y^{- 8})}^{\frac{3}{4}}$

Step 1

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

${(16 x^{16} \frac{1}{y^{8}})}^{\frac{3}{4}}$

Step 2

Multiply $16 x^{16} \frac{1}{y^{8}}$ .

Combine $16$ and $\frac{1}{y^{8}}$ .

${(x^{16} \frac{16}{y^{8}})}^{\frac{3}{4}}$

Combine $x^{16}$ and $\frac{16}{y^{8}}$ .

${(\frac{x^{16} \cdot 16}{y^{8}})}^{\frac{3}{4}}$

Step 3

Move $16$ to the left of $x^{16}$ .

${(\frac{16 \cdot x^{16}}{y^{8}})}^{\frac{3}{4}}$

Step 4

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

Apply the product rule to $\frac{16 x^{16}}{y^{8}}$ .

$\frac{{(16 x^{16})}^{\frac{3}{4}}}{{(y^{8})}^{\frac{3}{4}}}$

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

$\frac{16^{\frac{3}{4}} {(x^{16})}^{\frac{3}{4}}}{{(y^{8})}^{\frac{3}{4}}}$

Step 5

Simplify the numerator.

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

$\frac{{(2^{4})}^{\frac{3}{4}} {(x^{16})}^{\frac{3}{4}}}{{(y^{8})}^{\frac{3}{4}}}$

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

$\frac{2^{4 (\frac{3}{4})} {(x^{16})}^{\frac{3}{4}}}{{(y^{8})}^{\frac{3}{4}}}$

Cancel the common factor of $4$ .

Cancel the common factor.

$\frac{2^{4 (\frac{3}{4})} {(x^{16})}^{\frac{3}{4}}}{{(y^{8})}^{\frac{3}{4}}}$

Rewrite the expression.

$\frac{2^{3} {(x^{16})}^{\frac{3}{4}}}{{(y^{8})}^{\frac{3}{4}}}$

Raise $2$ to the power of $3$ .

$\frac{8 {(x^{16})}^{\frac{3}{4}}}{{(y^{8})}^{\frac{3}{4}}}$

Multiply the exponents in ${(x^{16})}^{\frac{3}{4}}$ .

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

$\frac{8 x^{16 (\frac{3}{4})}}{{(y^{8})}^{\frac{3}{4}}}$

Cancel the common factor of $4$ .

Factor $4$ out of $16$ .

$\frac{8 x^{4 (4) \frac{3}{4}}}{{(y^{8})}^{\frac{3}{4}}}$

Cancel the common factor.

$\frac{8 x^{4 \cdot 4 \frac{3}{4}}}{{(y^{8})}^{\frac{3}{4}}}$

Rewrite the expression.

$\frac{8 x^{4 \cdot 3}}{{(y^{8})}^{\frac{3}{4}}}$

Multiply $4$ by $3$ .

$\frac{8 x^{12}}{{(y^{8})}^{\frac{3}{4}}}$

Step 6

Multiply the exponents in ${(y^{8})}^{\frac{3}{4}}$ .

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

$\frac{8 x^{12}}{y^{8 (\frac{3}{4})}}$

Cancel the common factor of $4$ .

Factor $4$ out of $8$ .

$\frac{8 x^{12}}{y^{4 (2) \frac{3}{4}}}$

Cancel the common factor.

$\frac{8 x^{12}}{y^{4 \cdot 2 \frac{3}{4}}}$

Rewrite the expression.

$\frac{8 x^{12}}{y^{2 \cdot 3}}$

Multiply $2$ by $3$ .

$\frac{8 x^{12}}{y^{6}}$

Simplify (16x^16y^-8)^(3/4)

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