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

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

Step 1

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

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

Step 2

Simplify the denominator.

Apply the product rule to $- 32 x^{5}$ .

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

Rewrite $- 32$ as ${(- 2)}^{5}$ .

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

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

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

Cancel the common factor of $5$ .

Cancel the common factor.

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

Rewrite the expression.

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

Evaluate the exponent.

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

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

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

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

Cancel the common factor of $5$ .

Cancel the common factor.

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

Rewrite the expression.

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

Simplify.

$\frac{1}{- 2 x}$

Step 3

Move the negative in front of the fraction.

$- \frac{1}{2 x}$