Evaluate (125/8)^(-4/3)

${(\frac{125}{8})}^{- \frac{4}{3}}$

Step 1

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

${(\frac{8}{125})}^{\frac{4}{3}}$

Step 2

Apply the product rule to $\frac{8}{125}$ .

$\frac{8^{\frac{4}{3}}}{125^{\frac{4}{3}}}$

Step 3

Simplify the numerator.

Rewrite $8$ as $2^{3}$ .

$\frac{{(2^{3})}^{\frac{4}{3}}}{125^{\frac{4}{3}}}$

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

$\frac{2^{3 (\frac{4}{3})}}{125^{\frac{4}{3}}}$

Cancel the common factor of $3$ .

Cancel the common factor.

$\frac{2^{3 (\frac{4}{3})}}{125^{\frac{4}{3}}}$

Rewrite the expression.

$\frac{2^{4}}{125^{\frac{4}{3}}}$

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

$\frac{16}{125^{\frac{4}{3}}}$

Step 4

Simplify the denominator.

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

$\frac{16}{{(5^{3})}^{\frac{4}{3}}}$

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

$\frac{16}{5^{3 (\frac{4}{3})}}$

Cancel the common factor of $3$ .

Cancel the common factor.

$\frac{16}{5^{3 (\frac{4}{3})}}$

Rewrite the expression.

$\frac{16}{5^{4}}$

Raise $5$ to the power of $4$ .

$\frac{16}{625}$

Step 5

The result can be shown in multiple forms.

Exact Form:

$\frac{16}{625}$

Decimal Form:

$0.0256$