Simplify (1/(125x^3))^(-1/3)

${(\frac{1}{125 x^{3}})}^{- \frac{1}{3}}$

Step 1

Change the sign of the exponent by rewriting the base as its reciprocal.

${(125 x^{3})}^{\frac{1}{3}}$

Step 2

Simplify the expression.

Apply the product rule to $125 x^{3}$ .

$125^{\frac{1}{3}} {(x^{3})}^{\frac{1}{3}}$

Rewrite $125$ as $5^{3}$ .

${(5^{3})}^{\frac{1}{3}} {(x^{3})}^{\frac{1}{3}}$

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

$5^{3 (\frac{1}{3})} {(x^{3})}^{\frac{1}{3}}$

Step 3

Cancel the common factor of $3$ .

Cancel the common factor.

$5^{3 (\frac{1}{3})} {(x^{3})}^{\frac{1}{3}}$

Rewrite the expression.

$5^{1} {(x^{3})}^{\frac{1}{3}}$

Step 4

Evaluate the exponent.

$5 {(x^{3})}^{\frac{1}{3}}$

Step 5

Multiply the exponents in ${(x^{3})}^{\frac{1}{3}}$ .

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

$5 x^{3 (\frac{1}{3})}$

Cancel the common factor of $3$ .

Cancel the common factor.

$5 x^{3 (\frac{1}{3})}$

Rewrite the expression.

$5 x^{1}$

Step 6

Simplify.

$5 x$