Simplify (-3(v^-1)^5)/(2v^-1)

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

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.

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

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

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

Multiply $- 1$ by $5$ .

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

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

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

Combine exponents.

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

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

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

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

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

Factor $v$ out of $- 3 v$ .

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

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

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

Cancel the common factor.

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

Rewrite the expression.

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

Move the negative in front of the fraction.

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

Step 3

Multiply the numerator by the reciprocal of the denominator.

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

Step 4

Multiply $\frac{1}{2}$ by $\frac{3}{v^{4}}$ .

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