Finite Math Examples

${(\frac{a^{3}}{5 m})}^{- 4}$

Step 1

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

${(\frac{5 m}{a^{3}})}^{4}$

Step 2

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

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Step 2.1

Apply the product rule to $\frac{5 m}{a^{3}}$ .

$\frac{{(5 m)}^{4}}{{(a^{3})}^{4}}$

Step 2.2

Apply the product rule to $5 m$ .

$\frac{5^{4} m^{4}}{{(a^{3})}^{4}}$

Step 3

Raise $5$ to the power of $4$ .

$\frac{625 m^{4}}{{(a^{3})}^{4}}$

Step 4

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

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Step 4.1

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

$\frac{625 m^{4}}{a^{3 \cdot 4}}$

Step 4.2

Multiply $3$ by $4$ .

$\frac{625 m^{4}}{a^{12}}$