Algebra Examples

${(- \frac{w^{3}}{6})}^{- 2}$

Step 1

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

${(- \frac{6}{w^{3}})}^{2}$

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 $- \frac{6}{w^{3}}$ .

${(- 1)}^{2} {(\frac{6}{w^{3}})}^{2}$

Step 2.2

Apply the product rule to $\frac{6}{w^{3}}$ .

${(- 1)}^{2} \frac{6^{2}}{{(w^{3})}^{2}}$

Step 3

Raise $- 1$ to the power of $2$ .

$1 \frac{6^{2}}{{(w^{3})}^{2}}$

Step 4

Multiply $\frac{6^{2}}{{(w^{3})}^{2}}$ by $1$ .

$\frac{6^{2}}{{(w^{3})}^{2}}$

Step 5

Raise $6$ to the power of $2$ .

$\frac{36}{{(w^{3})}^{2}}$

Step 6

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

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Step 6.1

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

$\frac{36}{w^{3 \cdot 2}}$

Step 6.2

Multiply $3$ by $2$ .

$\frac{36}{w^{6}}$