Evaluate (1/125)^(1/3)

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

Step 1

Simplify the expression.

Apply the product rule to $\frac{1}{125}$ .

$\frac{1^{\frac{1}{3}}}{125^{\frac{1}{3}}}$

One to any power is one.

$\frac{1}{125^{\frac{1}{3}}}$

Step 2

Simplify the denominator.

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

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

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

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

Cancel the common factor of $3$ .

Cancel the common factor.

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

Rewrite the expression.

$\frac{1}{5^{1}}$

Evaluate the exponent.

$\frac{1}{5}$

Step 3

The result can be shown in multiple forms.

Exact Form:

$\frac{1}{5}$

Decimal Form:

$0.2$