Simplify (x^3)/((x^-6)^3)

$\frac{x^{3}}{{(x^{- 6})}^{3}}$

Step 1

Simplify the denominator.

Multiply the exponents in ${(x^{- 6})}^{3}$ .

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

$\frac{x^{3}}{x^{- 6 \cdot 3}}$

Multiply $- 6$ by $3$ .

$\frac{x^{3}}{x^{- 18}}$

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

$\frac{x^{3}}{\frac{1}{x^{18}}}$

Step 2

Multiply the numerator by the reciprocal of the denominator.

$x^{3} x^{18}$

Step 3

Multiply $x^{3}$ by $x^{18}$ by adding the exponents.

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

$x^{3 + 18}$

Add $3$ and $18$ .

$x^{21}$