Simplify (x^-3*y^3)^-7

${(x^{- 3} \cdot y^{3})}^{- 7}$

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

${(\frac{1}{x^{3}} \cdot y^{3})}^{- 7}$

Combine $\frac{1}{x^{3}}$ and $y^{3}$ .

${(\frac{y^{3}}{x^{3}})}^{- 7}$

Change the sign of the exponent by rewriting the base as its reciprocal.

${(\frac{x^{3}}{y^{3}})}^{7}$

Apply the product rule to $\frac{x^{3}}{y^{3}}$ .

$\frac{{(x^{3})}^{7}}{{(y^{3})}^{7}}$

Multiply the exponents in ${(x^{3})}^{7}$ .

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

$\frac{x^{3 \cdot 7}}{{(y^{3})}^{7}}$

Multiply $3$ by $7$ .

$\frac{x^{21}}{{(y^{3})}^{7}}$

Multiply the exponents in ${(y^{3})}^{7}$ .

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

$\frac{x^{21}}{y^{3 \cdot 7}}$

Multiply $3$ by $7$ .

$\frac{x^{21}}{y^{21}}$