Simplify ((x^3)/(x^-1))^(-1/4)

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

Step 1

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

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

Step 2

Multiply $x^{3}$ by $x$ by adding the exponents.

Multiply $x^{3}$ by $x$ .

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

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

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

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

Add $3$ and $1$ .

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

Step 3

Multiply the exponents in ${(x^{4})}^{- \frac{1}{4}}$ .

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

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

Cancel the common factor of $4$ .

Move the leading negative in $- \frac{1}{4}$ into the numerator.

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

Cancel the common factor.

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

Rewrite the expression.

$x^{- 1}$

Step 4

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

$\frac{1}{x}$