Basic Math Examples

${(\frac{125}{8})}^{\frac{- 2}{3}}$

Step 1

Move the negative in front of the fraction.

${(\frac{125}{8})}^{- \frac{2}{3}}$

Step 2

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

${(\frac{8}{125})}^{\frac{2}{3}}$

Step 3

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

$\frac{8^{\frac{2}{3}}}{125^{\frac{2}{3}}}$

Step 4

Simplify the numerator.

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Step 4.1

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

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

Step 4.2

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

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

Step 4.3

Cancel the common factor of $3$ .

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Step 4.3.1

Cancel the common factor.

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

Step 4.3.2

Rewrite the expression.

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

Step 4.4

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

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

Step 5

Simplify the denominator.

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Step 5.1

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

$\frac{4}{{(5^{3})}^{\frac{2}{3}}}$

Step 5.2

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

$\frac{4}{5^{3 (\frac{2}{3})}}$

Step 5.3

Cancel the common factor of $3$ .

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Step 5.3.1

Cancel the common factor.

$\frac{4}{5^{3 (\frac{2}{3})}}$

Step 5.3.2

Rewrite the expression.

$\frac{4}{5^{2}}$

Step 5.4

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

$\frac{4}{25}$

Step 6

The result can be shown in multiple forms.

Exact Form:

$\frac{4}{25}$

Decimal Form:

$0.16$