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

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

Step 1

Multiply $v^{- 4}$ by $v^{3}$ by adding the exponents.

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

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

Add $- 4$ and $3$ .

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

Step 2

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

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

Step 3

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

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