Precalculus Examples

${(m^{- 3} n^{9})}^{- 4}$

Step 1

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

${(\frac{1}{m^{3}} n^{9})}^{- 4}$

Step 2

Combine $\frac{1}{m^{3}}$ and $n^{9}$ .

${(\frac{n^{9}}{m^{3}})}^{- 4}$

Step 3

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

${(\frac{m^{3}}{n^{9}})}^{4}$

Step 4

Apply the product rule to $\frac{m^{3}}{n^{9}}$ .

$\frac{{(m^{3})}^{4}}{{(n^{9})}^{4}}$

Step 5

Multiply the exponents in ${(m^{3})}^{4}$ .

Tap for more steps...

Step 5.1

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

$\frac{m^{3 \cdot 4}}{{(n^{9})}^{4}}$

Step 5.2

Multiply $3$ by $4$ .

$\frac{m^{12}}{{(n^{9})}^{4}}$

Step 6

Multiply the exponents in ${(n^{9})}^{4}$ .

Tap for more steps...

Step 6.1

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

$\frac{m^{12}}{n^{9 \cdot 4}}$

Step 6.2

Multiply $9$ by $4$ .

$\frac{m^{12}}{n^{36}}$