Algebra Examples

${(\frac{m^{- 3} n^{4}}{n^{- 2}})}^{4}$

Step 1

Move $m^{- 3}$ to the denominator using the negative exponent rule $b^{- n} = \frac{1}{b^{n}}$ .

${(\frac{n^{4}}{n^{- 2} m^{3}})}^{4}$

Step 2

Move $n^{- 2}$ to the numerator using the negative exponent rule $\frac{1}{b^{- n}} = b^{n}$ .

${(\frac{n^{4} n^{2}}{m^{3}})}^{4}$

Step 3

Multiply $n^{4}$ by $n^{2}$ by adding the exponents.

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Step 3.1

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

${(\frac{n^{4 + 2}}{m^{3}})}^{4}$

Step 3.2

Add $4$ and $2$ .

${(\frac{n^{6}}{m^{3}})}^{4}$

Step 4

Apply the product rule to $\frac{n^{6}}{m^{3}}$ .

$\frac{{(n^{6})}^{4}}{{(m^{3})}^{4}}$

Step 5

Multiply the exponents in ${(n^{6})}^{4}$ .

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Step 5.1

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

$\frac{n^{6 \cdot 4}}{{(m^{3})}^{4}}$

Step 5.2

Multiply $6$ by $4$ .

$\frac{n^{24}}{{(m^{3})}^{4}}$

Step 6

Multiply the exponents in ${(m^{3})}^{4}$ .

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Step 6.1

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

$\frac{n^{24}}{m^{3 \cdot 4}}$

Step 6.2

Multiply $3$ by $4$ .

$\frac{n^{24}}{m^{12}}$