Pre-Algebra Examples

${(6 m^{- 4} n^{7})}^{2}$

Step 1

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

${(6 \frac{1}{m^{4}} n^{7})}^{2}$

Step 2

Combine $6$ and $\frac{1}{m^{4}}$ .

${(\frac{6}{m^{4}} n^{7})}^{2}$

Step 3

Combine $\frac{6}{m^{4}}$ and $n^{7}$ .

${(\frac{6 n^{7}}{m^{4}})}^{2}$

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 $\frac{6 n^{7}}{m^{4}}$ .

$\frac{{(6 n^{7})}^{2}}{{(m^{4})}^{2}}$

Step 4.2

Apply the product rule to $6 n^{7}$ .

$\frac{6^{2} {(n^{7})}^{2}}{{(m^{4})}^{2}}$

Step 5

Simplify the numerator.

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Step 5.1

Raise $6$ to the power of $2$ .

$\frac{36 {(n^{7})}^{2}}{{(m^{4})}^{2}}$

Step 5.2

Multiply the exponents in ${(n^{7})}^{2}$ .

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Step 5.2.1

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

$\frac{36 n^{7 \cdot 2}}{{(m^{4})}^{2}}$

Step 5.2.2

Multiply $7$ by $2$ .

$\frac{36 n^{14}}{{(m^{4})}^{2}}$

Step 6

Multiply the exponents in ${(m^{4})}^{2}$ .

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Step 6.1

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

$\frac{36 n^{14}}{m^{4 \cdot 2}}$

Step 6.2

Multiply $4$ by $2$ .

$\frac{36 n^{14}}{m^{8}}$