Algebra Examples

${(m^{3} n^{- 5} m^{- 1})}^{- 3}$

Step 1

Multiply $m^{3}$ by $m^{- 1}$ by adding the exponents.

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Step 1.1

Move $m^{- 1}$ .

${(m^{- 1} m^{3} n^{- 5})}^{- 3}$

Step 1.2

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

${(m^{- 1 + 3} n^{- 5})}^{- 3}$

Step 1.3

Add $- 1$ and $3$ .

${(m^{2} n^{- 5})}^{- 3}$

Step 2

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

${(m^{2} \frac{1}{n^{5}})}^{- 3}$

Step 3

Combine $m^{2}$ and $\frac{1}{n^{5}}$ .

${(\frac{m^{2}}{n^{5}})}^{- 3}$

Step 4

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

${(\frac{n^{5}}{m^{2}})}^{3}$

Step 5

Apply the product rule to $\frac{n^{5}}{m^{2}}$ .

$\frac{{(n^{5})}^{3}}{{(m^{2})}^{3}}$

Step 6

Multiply the exponents in ${(n^{5})}^{3}$ .

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Step 6.1

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

$\frac{n^{5 \cdot 3}}{{(m^{2})}^{3}}$

Step 6.2

Multiply $5$ by $3$ .

$\frac{n^{15}}{{(m^{2})}^{3}}$

Step 7

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

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Step 7.1

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

$\frac{n^{15}}{m^{2 \cdot 3}}$

Step 7.2

Multiply $2$ by $3$ .

$\frac{n^{15}}{m^{6}}$