Evaluate (125/216)^(2/3)

${(\frac{125}{216})}^{\frac{2}{3}}$

Step 1

Apply the product rule to $\frac{125}{216}$ .

$\frac{125^{\frac{2}{3}}}{216^{\frac{2}{3}}}$

Step 2

Simplify the numerator.

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

$\frac{{(5^{3})}^{\frac{2}{3}}}{216^{\frac{2}{3}}}$

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

$\frac{5^{3 (\frac{2}{3})}}{216^{\frac{2}{3}}}$

Cancel the common factor of $3$ .

Cancel the common factor.

$\frac{5^{3 (\frac{2}{3})}}{216^{\frac{2}{3}}}$

Rewrite the expression.

$\frac{5^{2}}{216^{\frac{2}{3}}}$

Raise $5$ to the power of $2$ .

$\frac{25}{216^{\frac{2}{3}}}$

Step 3

Simplify the denominator.

Rewrite $216$ as $6^{3}$ .

$\frac{25}{{(6^{3})}^{\frac{2}{3}}}$

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

$\frac{25}{6^{3 (\frac{2}{3})}}$

Cancel the common factor of $3$ .

Cancel the common factor.

$\frac{25}{6^{3 (\frac{2}{3})}}$

Rewrite the expression.

$\frac{25}{6^{2}}$

Raise $6$ to the power of $2$ .

$\frac{25}{36}$

Step 4

The result can be shown in multiple forms.

Exact Form:

$\frac{25}{36}$

Decimal Form:

$0.69\overline{4}$