Basic Math Examples

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

Step 1

Move the negative in front of the fraction.

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

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 $- \frac{w^{3}}{2 v}$ .

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

Step 2.2

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

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

Step 2.3

Apply the product rule to $2 v$ .

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

Step 3

Raise $- 1$ to the power of $3$ .

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

Step 4

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

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Step 4.1

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

$- \frac{w^{3 \cdot 3}}{2^{3} v^{3}}$

Step 4.2

Multiply $3$ by $3$ .

$- \frac{w^{9}}{2^{3} v^{3}}$

Step 5

Raise $2$ to the power of $3$ .

$- \frac{w^{9}}{8 v^{3}}$