Basic Math Examples

${(32 k^{5} m^{- 10})}^{\frac{1}{5}}$

Step 1

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

${(32 k^{5} \frac{1}{m^{10}})}^{\frac{1}{5}}$

Step 2

Multiply $32 k^{5} \frac{1}{m^{10}}$ .

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Step 2.1

Combine $32$ and $\frac{1}{m^{10}}$ .

${(k^{5} \frac{32}{m^{10}})}^{\frac{1}{5}}$

Step 2.2

Combine $k^{5}$ and $\frac{32}{m^{10}}$ .

${(\frac{k^{5} \cdot 32}{m^{10}})}^{\frac{1}{5}}$

Step 3

Move $32$ to the left of $k^{5}$ .

${(\frac{32 \cdot k^{5}}{m^{10}})}^{\frac{1}{5}}$

Step 4

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

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Step 4.1

Apply the product rule to $\frac{32 k^{5}}{m^{10}}$ .

$\frac{{(32 k^{5})}^{\frac{1}{5}}}{{(m^{10})}^{\frac{1}{5}}}$

Step 4.2

Apply the product rule to $32 k^{5}$ .

$\frac{32^{\frac{1}{5}} {(k^{5})}^{\frac{1}{5}}}{{(m^{10})}^{\frac{1}{5}}}$

Step 5

Simplify the numerator.

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Step 5.1

Rewrite $32$ as $2^{5}$ .

$\frac{{(2^{5})}^{\frac{1}{5}} {(k^{5})}^{\frac{1}{5}}}{{(m^{10})}^{\frac{1}{5}}}$

Step 5.2

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

$\frac{2^{5 (\frac{1}{5})} {(k^{5})}^{\frac{1}{5}}}{{(m^{10})}^{\frac{1}{5}}}$

Step 5.3

Cancel the common factor of $5$ .

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Step 5.3.1

Cancel the common factor.

$\frac{2^{5 (\frac{1}{5})} {(k^{5})}^{\frac{1}{5}}}{{(m^{10})}^{\frac{1}{5}}}$

Step 5.3.2

Rewrite the expression.

$\frac{2^{1} {(k^{5})}^{\frac{1}{5}}}{{(m^{10})}^{\frac{1}{5}}}$

Step 5.4

Evaluate the exponent.

$\frac{2 {(k^{5})}^{\frac{1}{5}}}{{(m^{10})}^{\frac{1}{5}}}$

Step 5.5

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

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Step 5.5.1

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

$\frac{2 k^{5 (\frac{1}{5})}}{{(m^{10})}^{\frac{1}{5}}}$

Step 5.5.2

Cancel the common factor of $5$ .

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Step 5.5.2.1

Cancel the common factor.

$\frac{2 k^{5 (\frac{1}{5})}}{{(m^{10})}^{\frac{1}{5}}}$

Step 5.5.2.2

Rewrite the expression.

$\frac{2 k^{1}}{{(m^{10})}^{\frac{1}{5}}}$

Step 5.6

Simplify.

$\frac{2 k}{{(m^{10})}^{\frac{1}{5}}}$

Step 6

Multiply the exponents in ${(m^{10})}^{\frac{1}{5}}$ .

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Step 6.1

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

$\frac{2 k}{m^{10 (\frac{1}{5})}}$

Step 6.2

Cancel the common factor of $5$ .

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Step 6.2.1

Factor $5$ out of $10$ .

$\frac{2 k}{m^{5 (2) \frac{1}{5}}}$

Step 6.2.2

Cancel the common factor.

$\frac{2 k}{m^{5 \cdot 2 \frac{1}{5}}}$

Step 6.2.3

Rewrite the expression.

$\frac{2 k}{m^{2}}$