Basic Math Examples

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

Step 1

Use the power rule ${(a b)}^{n} = a^{n} b^{n}$ to distribute the exponent.

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Step 1.1

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

${(- 1)}^{\frac{4}{3}} {(\frac{8}{125})}^{\frac{4}{3}}$

Step 1.2

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

${(- 1)}^{\frac{4}{3}} \frac{8^{\frac{4}{3}}}{125^{\frac{4}{3}}}$

Step 2

Reduce the expression by cancelling the common factors.

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Step 2.1

Rewrite $- 1$ as ${(- 1)}^{3}$ .

${({(- 1)}^{3})}^{\frac{4}{3}} \frac{8^{\frac{4}{3}}}{125^{\frac{4}{3}}}$

Step 2.2

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

${(- 1)}^{3 (\frac{4}{3})} \frac{8^{\frac{4}{3}}}{125^{\frac{4}{3}}}$

Step 2.3

Cancel the common factor of $3$ .

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Step 2.3.1

Cancel the common factor.

${(- 1)}^{3 (\frac{4}{3})} \frac{8^{\frac{4}{3}}}{125^{\frac{4}{3}}}$

Step 2.3.2

Rewrite the expression.

${(- 1)}^{4} \frac{8^{\frac{4}{3}}}{125^{\frac{4}{3}}}$

Step 2.4

Simplify the expression.

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Step 2.4.1

Raise $- 1$ to the power of $4$ .

$1 \frac{8^{\frac{4}{3}}}{125^{\frac{4}{3}}}$

Step 2.4.2

Multiply $\frac{8^{\frac{4}{3}}}{125^{\frac{4}{3}}}$ by $1$ .

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

Step 3

Simplify the numerator.

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Step 3.1

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

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

Step 3.2

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

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

Step 3.3

Cancel the common factor of $3$ .

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Step 3.3.1

Cancel the common factor.

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

Step 3.3.2

Rewrite the expression.

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

Step 3.4

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

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

Step 4

Simplify the denominator.

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Step 4.1

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

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

Step 4.2

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

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

Step 4.3

Cancel the common factor of $3$ .

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Step 4.3.1

Cancel the common factor.

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

Step 4.3.2

Rewrite the expression.

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

Step 4.4

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:

$0.0256$