Simplify 4v^(2/3)*v^-1

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

Multiply $v^{\frac{2}{3}}$ by $v^{- 1}$ by adding the exponents.

Move $v^{- 1}$ .

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

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

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

To write $- 1$ as a fraction with a common denominator, multiply by $\frac{3}{3}$ .

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

Combine $- 1$ and $\frac{3}{3}$ .

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

Combine the numerators over the common denominator.

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

Simplify the numerator.

Multiply $- 1$ by $3$ .

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

Add $- 3$ and $2$ .

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

Move the negative in front of the fraction.

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

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

$4 \frac{1}{v^{\frac{1}{3}}}$

Combine $4$ and $\frac{1}{v^{\frac{1}{3}}}$ .

$\frac{4}{v^{\frac{1}{3}}}$