Trigonometry Examples

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

Step 1

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

${(3 \frac{1}{m^{4}} n^{- 3})}^{- 2}$

Step 2

Combine $3$ and $\frac{1}{m^{4}}$ .

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

Step 3

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

${(\frac{3}{m^{4}} \cdot \frac{1}{n^{3}})}^{- 2}$

Step 4

Combine.

${(\frac{3 \cdot 1}{m^{4} n^{3}})}^{- 2}$

Step 5

Multiply $3$ by $1$ .

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

Step 6

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

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

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 $\frac{m^{4} n^{3}}{3}$ .

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

Step 7.2

Apply the product rule to $m^{4} n^{3}$ .

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

Step 8

Simplify the numerator.

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Step 8.1

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

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Step 8.1.1

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

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

Step 8.1.2

Multiply $4$ by $2$ .

$\frac{m^{8} {(n^{3})}^{2}}{3^{2}}$

Step 8.2

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

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Step 8.2.1

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

$\frac{m^{8} n^{3 \cdot 2}}{3^{2}}$

Step 8.2.2

Multiply $3$ by $2$ .

$\frac{m^{8} n^{6}}{3^{2}}$

Step 9

Raise $3$ to the power of $2$ .

$\frac{m^{8} n^{6}}{9}$