Simplify the Radical Expression (32x^-10y^35)^(4/5)

${(32 x^{- 10} y^{35})}^{\frac{4}{5}}$

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

${(32 \frac{1}{x^{10}} y^{35})}^{\frac{4}{5}}$

Combine $32$ and $\frac{1}{x^{10}}$ .

${(\frac{32}{x^{10}} y^{35})}^{\frac{4}{5}}$

Combine $\frac{32}{x^{10}}$ and $y^{35}$ .

${(\frac{32 y^{35}}{x^{10}})}^{\frac{4}{5}}$

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

Apply the product rule to $\frac{32 y^{35}}{x^{10}}$ .

$\frac{{(32 y^{35})}^{\frac{4}{5}}}{{(x^{10})}^{\frac{4}{5}}}$

Apply the product rule to $32 y^{35}$ .

$\frac{32^{\frac{4}{5}} {(y^{35})}^{\frac{4}{5}}}{{(x^{10})}^{\frac{4}{5}}}$

Simplify the numerator.

Rewrite $32$ as $2^{5}$ .

$\frac{{(2^{5})}^{\frac{4}{5}} {(y^{35})}^{\frac{4}{5}}}{{(x^{10})}^{\frac{4}{5}}}$

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

$\frac{2^{5 (\frac{4}{5})} {(y^{35})}^{\frac{4}{5}}}{{(x^{10})}^{\frac{4}{5}}}$

Cancel the common factor of $5$ .

Cancel the common factor.

$\frac{2^{5 (\frac{4}{5})} {(y^{35})}^{\frac{4}{5}}}{{(x^{10})}^{\frac{4}{5}}}$

Rewrite the expression.

$\frac{2^{4} {(y^{35})}^{\frac{4}{5}}}{{(x^{10})}^{\frac{4}{5}}}$

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

$\frac{16 {(y^{35})}^{\frac{4}{5}}}{{(x^{10})}^{\frac{4}{5}}}$

Multiply the exponents in ${(y^{35})}^{\frac{4}{5}}$ .

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

$\frac{16 y^{35 (\frac{4}{5})}}{{(x^{10})}^{\frac{4}{5}}}$

Cancel the common factor of $5$ .

Factor $5$ out of $35$ .

$\frac{16 y^{5 (7) \frac{4}{5}}}{{(x^{10})}^{\frac{4}{5}}}$

Cancel the common factor.

$\frac{16 y^{5 \cdot 7 \frac{4}{5}}}{{(x^{10})}^{\frac{4}{5}}}$

Rewrite the expression.

$\frac{16 y^{7 \cdot 4}}{{(x^{10})}^{\frac{4}{5}}}$

Multiply $7$ by $4$ .

$\frac{16 y^{28}}{{(x^{10})}^{\frac{4}{5}}}$

Multiply the exponents in ${(x^{10})}^{\frac{4}{5}}$ .

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

$\frac{16 y^{28}}{x^{10 (\frac{4}{5})}}$

Cancel the common factor of $5$ .

Factor $5$ out of $10$ .

$\frac{16 y^{28}}{x^{5 (2) \frac{4}{5}}}$

Cancel the common factor.

$\frac{16 y^{28}}{x^{5 \cdot 2 \frac{4}{5}}}$

Rewrite the expression.

$\frac{16 y^{28}}{x^{2 \cdot 4}}$

Multiply $2$ by $4$ .

$\frac{16 y^{28}}{x^{8}}$

Simplify the Radical Expression (32x^-10y^35)^(4/5)

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