Evaluate (64/125)^(1/3)

${(\frac{64}{125})}^{\frac{1}{3}}$

Step 1

Apply the product rule to $\frac{64}{125}$ .

$\frac{64^{\frac{1}{3}}}{125^{\frac{1}{3}}}$

Step 2

Simplify the numerator.

Rewrite $64$ as $4^{3}$ .

$\frac{{(4^{3})}^{\frac{1}{3}}}{125^{\frac{1}{3}}}$

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

$\frac{4^{3 (\frac{1}{3})}}{125^{\frac{1}{3}}}$

Cancel the common factor of $3$ .

Cancel the common factor.

$\frac{4^{3 (\frac{1}{3})}}{125^{\frac{1}{3}}}$

Rewrite the expression.

$\frac{4^{1}}{125^{\frac{1}{3}}}$

Evaluate the exponent.

$\frac{4}{125^{\frac{1}{3}}}$

Step 3

Simplify the denominator.

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

$\frac{4}{{(5^{3})}^{\frac{1}{3}}}$

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

$\frac{4}{5^{3 (\frac{1}{3})}}$

Cancel the common factor of $3$ .

Cancel the common factor.

$\frac{4}{5^{3 (\frac{1}{3})}}$

Rewrite the expression.

$\frac{4}{5^{1}}$

Evaluate the exponent.

$\frac{4}{5}$

Step 4

The result can be shown in multiple forms.

Exact Form:

$\frac{4}{5}$

Decimal Form:

$0.8$