Algebra Examples

$- \frac{3 {(v^{- 1})}^{5}}{2 v^{- 1}}$

Step 1

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

$- \frac{3 {(v^{- 1})}^{5} v}{2}$

Step 2

Simplify the numerator.

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Step 2.1

Multiply the exponents in ${(v^{- 1})}^{5}$ .

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Step 2.1.1

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

$- \frac{3 v^{- 1 \cdot 5} v}{2}$

Step 2.1.2

Multiply $- 1$ by $5$ .

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

Step 2.2

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

$- \frac{3 \frac{1}{v^{5}} v}{2}$

Step 2.3

Combine exponents.

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Step 2.3.1

Combine $3$ and $\frac{1}{v^{5}}$ .

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

Step 2.3.2

Combine $\frac{3}{v^{5}}$ and $v$ .

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

Step 2.4

Reduce the expression $\frac{3 v}{v^{5}}$ by cancelling the common factors.

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Step 2.4.1

Factor $v$ out of $3 v$ .

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

Step 2.4.2

Factor $v$ out of $v^{5}$ .

$- \frac{\frac{v \cdot 3}{v \cdot v^{4}}}{2}$

Step 2.4.3

Cancel the common factor.

$- \frac{\frac{v \cdot 3}{v \cdot v^{4}}}{2}$

Step 2.4.4

Rewrite the expression.

$- \frac{\frac{3}{v^{4}}}{2}$

Step 3

Multiply the numerator by the reciprocal of the denominator.

$- (\frac{3}{v^{4}} \cdot \frac{1}{2})$

Step 4

Combine.

$- \frac{3 \cdot 1}{v^{4} \cdot 2}$

Step 5

Simplify the expression.

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Step 5.1

Multiply $3$ by $1$ .

$- \frac{3}{v^{4} \cdot 2}$

Step 5.2

Move $2$ to the left of $v^{4}$ .

$- \frac{3}{2 v^{4}}$