Evaluate (125/64)^(2/3)

${(\frac{125}{64})}^{\frac{2}{3}}$

Step 1

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

$\frac{125^{\frac{2}{3}}}{64^{\frac{2}{3}}}$

Step 2

Simplify the numerator.

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

$\frac{{(5^{3})}^{\frac{2}{3}}}{64^{\frac{2}{3}}}$

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

$\frac{5^{3 (\frac{2}{3})}}{64^{\frac{2}{3}}}$

Cancel the common factor of $3$ .

Cancel the common factor.

$\frac{5^{3 (\frac{2}{3})}}{64^{\frac{2}{3}}}$

Rewrite the expression.

$\frac{5^{2}}{64^{\frac{2}{3}}}$

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

$\frac{25}{64^{\frac{2}{3}}}$

Step 3

Simplify the denominator.

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

$\frac{25}{{(4^{3})}^{\frac{2}{3}}}$

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

$\frac{25}{4^{3 (\frac{2}{3})}}$

Cancel the common factor of $3$ .

Cancel the common factor.

$\frac{25}{4^{3 (\frac{2}{3})}}$

Rewrite the expression.

$\frac{25}{4^{2}}$

Raise $4$ to the power of $2$ .

$\frac{25}{16}$

Step 4

The result can be shown in multiple forms.

Exact Form:

$\frac{25}{16}$

Decimal Form:

$1.5625$

Mixed Number Form:

$1 \frac{9}{16}$