Finite Math Examples

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

Step 1

Move $m^{- 9}$ to the denominator using the negative exponent rule $b^{- n} = \frac{1}{b^{n}}$ .

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

Step 2

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

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

Step 3

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

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

Step 4

Raise $3$ to the power of $4$ .

$81 {(m^{9})}^{4}$

Step 5

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

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Step 5.1

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

$81 m^{9 \cdot 4}$

Step 5.2

Multiply $9$ by $4$ .

$81 m^{36}$