Algebra Examples

$\frac{- 2 {(v^{- 1})}^{2}}{- 5 v}$

Step 1

Simplify the numerator.

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Step 1.1

Multiply the exponents in ${(v^{- 1})}^{2}$ .

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Step 1.1.1

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

$\frac{- 2 v^{- 1 \cdot 2}}{- 5 v}$

Step 1.1.2

Multiply $- 1$ by $2$ .

$\frac{- 2 v^{- 2}}{- 5 v}$

Step 1.2

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

$\frac{- 2 \frac{1}{v^{2}}}{- 5 v}$

Step 2

Combine $- 2$ and $\frac{1}{v^{2}}$ .

$\frac{\frac{- 2}{v^{2}}}{- 5 v}$

Step 3

Move the negative in front of the fraction.

$\frac{- \frac{2}{v^{2}}}{- 5 v}$

Step 4

Multiply the numerator by the reciprocal of the denominator.

$- \frac{2}{v^{2}} \cdot \frac{1}{- 5 v}$

Step 5

Move the negative in front of the fraction.

$- \frac{2}{v^{2}} (- \frac{1}{5 v})$

Step 6

Multiply $- \frac{2}{v^{2}} (- \frac{1}{5 v})$ .

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Step 6.1

Multiply $- 1$ by $- 1$ .

$1 \frac{2}{v^{2}} \frac{1}{5 v}$

Step 6.2

Multiply $\frac{2}{v^{2}}$ by $1$ .

$\frac{2}{v^{2}} \cdot \frac{1}{5 v}$

Step 6.3

Multiply $\frac{2}{v^{2}}$ by $\frac{1}{5 v}$ .

$\frac{2}{v^{2} (5 v)}$

Step 6.4

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

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Step 6.4.1

Move $v$ .

$\frac{2}{v \cdot v^{2} \cdot 5}$

Step 6.4.2

Multiply $v$ by $v^{2}$ .

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Step 6.4.2.1

Raise $v$ to the power of $1$ .

$\frac{2}{v^{1} v^{2} \cdot 5}$

Step 6.4.2.2

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

$\frac{2}{v^{1 + 2} \cdot 5}$

Step 6.4.3

Add $1$ and $2$ .

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

Step 7

Move $5$ to the left of $v^{3}$ .

$\frac{2}{5 v^{3}}$