Algebra Examples

${(- 7 m^{- 2} n^{- 1})}^{- 2}$

Step 1

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

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

Step 2

Combine $- 7$ and $\frac{1}{m^{2}}$ .

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

Step 3

Move the negative in front of the fraction.

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

Step 4

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

${(- \frac{7}{m^{2}} \cdot \frac{1}{n})}^{- 2}$

Step 5

Multiply $\frac{1}{n}$ by $\frac{7}{m^{2}}$ .

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

Step 6

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

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

Step 7

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

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Step 7.1

Apply the product rule to $- \frac{n m^{2}}{7}$ .

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

Step 7.2

Apply the product rule to $\frac{n m^{2}}{7}$ .

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

Step 7.3

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

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

Step 8

Raise $- 1$ to the power of $2$ .

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

Step 9

Multiply $\frac{n^{2} {(m^{2})}^{2}}{7^{2}}$ by $1$ .

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

Step 10

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

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Step 10.1

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

$\frac{n^{2} m^{2 \cdot 2}}{7^{2}}$

Step 10.2

Multiply $2$ by $2$ .

$\frac{n^{2} m^{4}}{7^{2}}$

Step 11

Raise $7$ to the power of $2$ .

$\frac{n^{2} m^{4}}{49}$