Basic Math Examples

${(m^{- 3} n^{5})}^{- \frac{1}{3}}$

Step 1

Rewrite the expression using the negative exponent rule $b^{- n} = \frac{1}{b^{n}}$ .

${(\frac{1}{m^{3}} n^{5})}^{- \frac{1}{3}}$

Step 2

Combine $\frac{1}{m^{3}}$ and $n^{5}$ .

${(\frac{n^{5}}{m^{3}})}^{- \frac{1}{3}}$

Step 3

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

${(\frac{m^{3}}{n^{5}})}^{\frac{1}{3}}$

Step 4

Apply the product rule to $\frac{m^{3}}{n^{5}}$ .

$\frac{{(m^{3})}^{\frac{1}{3}}}{{(n^{5})}^{\frac{1}{3}}}$

Step 5

Simplify the numerator.

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Step 5.1

Multiply the exponents in ${(m^{3})}^{\frac{1}{3}}$ .

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Step 5.1.1

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

$\frac{m^{3 (\frac{1}{3})}}{{(n^{5})}^{\frac{1}{3}}}$

Step 5.1.2

Cancel the common factor of $3$ .

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Step 5.1.2.1

Cancel the common factor.

$\frac{m^{3 (\frac{1}{3})}}{{(n^{5})}^{\frac{1}{3}}}$

Step 5.1.2.2

Rewrite the expression.

$\frac{m^{1}}{{(n^{5})}^{\frac{1}{3}}}$

Step 5.2

Simplify.

$\frac{m}{{(n^{5})}^{\frac{1}{3}}}$

Step 6

Multiply the exponents in ${(n^{5})}^{\frac{1}{3}}$ .

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Step 6.1

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

$\frac{m}{n^{5 (\frac{1}{3})}}$

Step 6.2

Combine $5$ and $\frac{1}{3}$ .

$\frac{m}{n^{\frac{5}{3}}}$