Simplify (2x^3)/((x^-1)^3)

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

Step 1

Simplify the denominator.

Multiply the exponents in ${(x^{- 1})}^{3}$ .

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

$\frac{2 x^{3}}{x^{- 1 \cdot 3}}$

Multiply $- 1$ by $3$ .

$\frac{2 x^{3}}{x^{- 3}}$

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

$\frac{2 x^{3}}{\frac{1}{x^{3}}}$

Step 2

Multiply the numerator by the reciprocal of the denominator.

$2 x^{3} x^{3}$

Step 3

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

Move $x^{3}$ .

$2 (x^{3} x^{3})$

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

$2 x^{3 + 3}$

Add $3$ and $3$ .

$2 x^{6}$