Algebra Examples

${(m^{- 1} n^{- 2})}^{3}$

Step 1

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

${(\frac{1}{m} n^{- 2})}^{3}$

Step 2

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

${(\frac{1}{m} \cdot \frac{1}{n^{2}})}^{3}$

Step 3

Combine.

${(\frac{1 \cdot 1}{m n^{2}})}^{3}$

Step 4

Multiply $1$ by $1$ .

${(\frac{1}{m n^{2}})}^{3}$

Step 5

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

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Step 5.1

Apply the product rule to $\frac{1}{m n^{2}}$ .

$\frac{1^{3}}{{(m n^{2})}^{3}}$

Step 5.2

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

$\frac{1^{3}}{m^{3} {(n^{2})}^{3}}$

Step 6

One to any power is one.

$\frac{1}{m^{3} {(n^{2})}^{3}}$

Step 7

Multiply the exponents in ${(n^{2})}^{3}$ .

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Step 7.1

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

$\frac{1}{m^{3} n^{2 \cdot 3}}$

Step 7.2

Multiply $2$ by $3$ .

$\frac{1}{m^{3} n^{6}}$