Pre-Algebra Examples

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

Step 1

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

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

Step 2

Multiply $- 2 m^{2} \frac{1}{n^{4}}$ .

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Step 2.1

Combine $- 2$ and $\frac{1}{n^{4}}$ .

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

Step 2.2

Combine $m^{2}$ and $\frac{- 2}{n^{4}}$ .

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

Step 3

Move $- 2$ to the left of $m^{2}$ .

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

Step 4

Move the negative in front of the fraction.

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

Step 5

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

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

Step 6

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

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Step 6.1

Apply the product rule to $- \frac{n^{4}}{2 m^{2}}$ .

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

Step 6.2

Apply the product rule to $\frac{n^{4}}{2 m^{2}}$ .

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

Step 6.3

Apply the product rule to $2 m^{2}$ .

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

Step 7

Simplify the expression.

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Step 7.1

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

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

Step 7.2

Multiply $\frac{{(n^{4})}^{4}}{2^{4} {(m^{2})}^{4}}$ by $1$ .

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

Step 7.3

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

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Step 7.3.1

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

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

Step 7.3.2

Multiply $4$ by $4$ .

$\frac{n^{16}}{2^{4} {(m^{2})}^{4}}$

Step 8

Simplify the denominator.

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Step 8.1

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

$\frac{n^{16}}{16 {(m^{2})}^{4}}$

Step 8.2

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

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Step 8.2.1

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

$\frac{n^{16}}{16 m^{2 \cdot 4}}$

Step 8.2.2

Multiply $2$ by $4$ .

$\frac{n^{16}}{16 m^{8}}$