Algebra Examples

$\frac{{(4 v^{5})}^{3}}{- 2 v^{- 2}}$

Step 1

Move $v^{- 2}$ to the numerator using the negative exponent rule $\frac{1}{b^{- n}} = b^{n}$ .

$\frac{{(4 v^{5})}^{3} v^{2}}{- 2}$

Step 2

Simplify the numerator.

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Step 2.1

Apply the product rule to $4 v^{5}$ .

$\frac{4^{3} {(v^{5})}^{3} v^{2}}{- 2}$

Step 2.2

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

$\frac{64 {(v^{5})}^{3} v^{2}}{- 2}$

Step 2.3

Multiply the exponents in ${(v^{5})}^{3}$ .

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Step 2.3.1

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

$\frac{64 v^{5 \cdot 3} v^{2}}{- 2}$

Step 2.3.2

Multiply $5$ by $3$ .

$\frac{64 v^{15} v^{2}}{- 2}$

Step 2.4

Multiply $v^{15}$ by $v^{2}$ by adding the exponents.

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Step 2.4.1

Move $v^{2}$ .

$\frac{64 (v^{2} v^{15})}{- 2}$

Step 2.4.2

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

$\frac{64 v^{2 + 15}}{- 2}$

Step 2.4.3

Add $2$ and $15$ .

$\frac{64 v^{17}}{- 2}$

Step 3

Cancel the common factor of $64$ and $- 2$ .

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Step 3.1

Factor $2$ out of $64 v^{17}$ .

$\frac{2 (32 v^{17})}{- 2}$

Step 3.2

Move the negative one from the denominator of $\frac{32 v^{17}}{- 1}$ .

$- 1 \cdot (32 v^{17})$

Step 4

Rewrite $- 1 \cdot (32 v^{17})$ as $- (32 v^{17})$ .

$- (32 v^{17})$

Step 5

Multiply $32$ by $- 1$ .

$- 32 v^{17}$