Simplify ((x^-6)/(x^2))^3

${(\frac{x^{- 6}}{x^{2}})}^{3}$

Step 1

Move $x^{- 6}$ to the denominator using the negative exponent rule $b^{- n} = \frac{1}{b^{n}}$ .

${(\frac{1}{x^{2} x^{6}})}^{3}$

Step 2

Multiply $x^{2}$ by $x^{6}$ by adding the exponents.

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

${(\frac{1}{x^{2 + 6}})}^{3}$

Add $2$ and $6$ .

${(\frac{1}{x^{8}})}^{3}$

Step 3

Apply the product rule to $\frac{1}{x^{8}}$ .

$\frac{1^{3}}{{(x^{8})}^{3}}$

Step 4

One to any power is one.

$\frac{1}{{(x^{8})}^{3}}$

Step 5

Multiply the exponents in ${(x^{8})}^{3}$ .

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

$\frac{1}{x^{8 \cdot 3}}$

Multiply $8$ by $3$ .

$\frac{1}{x^{24}}$