Simplify (15(x^-2)^3)/(3(x^-4)^-3)

$\frac{15 {(x^{- 2})}^{3}}{3 {(x^{- 4})}^{- 3}}$

Move ${(x^{- 4})}^{- 3}$ to the numerator using the negative exponent rule $\frac{1}{b^{- n}} = b^{n}$ .

$\frac{15 {(x^{- 2})}^{3} {(x^{- 4})}^{3}}{3}$

Cancel the common factor of $15$ and $3$ .

Factor $3$ out of $15 {(x^{- 2})}^{3} {(x^{- 4})}^{3}$ .

$\frac{3 (5 {(x^{- 2})}^{3} {(x^{- 4})}^{3})}{3}$

Cancel the common factors.

Factor $3$ out of $3$ .

$\frac{3 (5 {(x^{- 2})}^{3} {(x^{- 4})}^{3})}{3 (1)}$

Cancel the common factor.

$\frac{3 (5 {(x^{- 2})}^{3} {(x^{- 4})}^{3})}{3 \cdot 1}$

Rewrite the expression.

$\frac{5 {(x^{- 2})}^{3} {(x^{- 4})}^{3}}{1}$

Divide $5 {(x^{- 2})}^{3} {(x^{- 4})}^{3}$ by $1$ .

$5 {(x^{- 2})}^{3} {(x^{- 4})}^{3}$

Multiply the exponents in ${(x^{- 2})}^{3}$ .

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

$5 x^{- 2 \cdot 3} {(x^{- 4})}^{3}$

Multiply $- 2$ by $3$ .

$5 x^{- 6} {(x^{- 4})}^{3}$

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

$5 \frac{1}{x^{6}} {(x^{- 4})}^{3}$

Combine $5$ and $\frac{1}{x^{6}}$ .

$\frac{5}{x^{6}} {(x^{- 4})}^{3}$

Multiply the exponents in ${(x^{- 4})}^{3}$ .

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

$\frac{5}{x^{6}} x^{- 4 \cdot 3}$

Multiply $- 4$ by $3$ .

$\frac{5}{x^{6}} x^{- 12}$

Cancel the common factor of $x^{- 12}$ .

Factor $x^{- 12}$ out of $x^{6}$ .

$\frac{5}{x^{- 12} x^{18}} x^{- 12}$

Cancel the common factor.

$\frac{5}{x^{- 12} x^{18}} x^{- 12}$

Rewrite the expression.

$\frac{5}{x^{18}}$