Finite Math Examples

${(3 w^{- 2})}^{4}$

Step 1

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

${(3 \frac{1}{w^{2}})}^{4}$

Step 2

Combine $3$ and $\frac{1}{w^{2}}$ .

${(\frac{3}{w^{2}})}^{4}$

Step 3

Simplify the expression.

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Step 3.1

Apply the product rule to $\frac{3}{w^{2}}$ .

$\frac{3^{4}}{{(w^{2})}^{4}}$

Step 3.2

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

$\frac{81}{{(w^{2})}^{4}}$

Step 3.3

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

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Step 3.3.1

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

$\frac{81}{w^{2 \cdot 4}}$

Step 3.3.2

Multiply $2$ by $4$ .

$\frac{81}{w^{8}}$