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

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

Move ${(x^{6})}^{- 2}$ to the denominator using the negative exponent rule $b^{- n} = \frac{1}{b^{n}}$ .

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

Multiply the exponents in ${(x^{6})}^{2}$ .

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

$\frac{1}{x^{3} x^{6 \cdot 2}}$

Multiply $6$ by $2$ .

$\frac{1}{x^{3} x^{12}}$

Multiply $x^{3}$ by $x^{12}$ by adding the exponents.

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

$\frac{1}{x^{3 + 12}}$

Add $3$ and $12$ .

$\frac{1}{x^{15}}$