Simplify (32x^20)^(-1/5)

${(32 x^{20})}^{- \frac{1}{5}}$

Step 1

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

$\frac{1}{{(32 x^{20})}^{\frac{1}{5}}}$

Step 2

Simplify the denominator.

Apply the product rule to $32 x^{20}$ .

$\frac{1}{32^{\frac{1}{5}} {(x^{20})}^{\frac{1}{5}}}$

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

$\frac{1}{{(2^{5})}^{\frac{1}{5}} {(x^{20})}^{\frac{1}{5}}}$

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

$\frac{1}{2^{5 (\frac{1}{5})} {(x^{20})}^{\frac{1}{5}}}$

Cancel the common factor of $5$ .

Cancel the common factor.

$\frac{1}{2^{5 (\frac{1}{5})} {(x^{20})}^{\frac{1}{5}}}$

Rewrite the expression.

$\frac{1}{2^{1} {(x^{20})}^{\frac{1}{5}}}$

Evaluate the exponent.

$\frac{1}{2 {(x^{20})}^{\frac{1}{5}}}$

Multiply the exponents in ${(x^{20})}^{\frac{1}{5}}$ .

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

$\frac{1}{2 x^{20 (\frac{1}{5})}}$

Cancel the common factor of $5$ .

Factor $5$ out of $20$ .

$\frac{1}{2 x^{5 (4) \frac{1}{5}}}$

Cancel the common factor.

$\frac{1}{2 x^{5 \cdot 4 \frac{1}{5}}}$

Rewrite the expression.

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