Answer
$\frac{1}{x^{12}y^{16}z^{20}}$
Work Step by Step
$$(\frac{x^{3}y^{4}z^{5}}{x^{-3}y^{-4}z^{-5}})^{-2}$$
Within the parentheses, group like terms and simplify.
$$=[(\frac{x^{3}}{x^{-3}})(\frac{y^{4}}{y^{-4}})(\frac{z^{5}}{z^{-5}})]^{-2}$$
When dividing exponential expressions with the same non-zero base, subtract the exponent of the denominator from the exponent of the numerator.
$$=(x^{(3-(-3))}y^{(4-(-4))}z^{(5-(-5))})^{-2}$$
$$=(x^{(3+3)}y^{(4+4)}z^{(5+5)})^{-2}$$
$$=(x^{6}y^{8}z^{10})^{-2}$$
When a product is raised to an exponent, raise each factor to that exponent.
$$=x^{(6\times(-2))}y^{(8\times(-2))}z^{(10\times(-2))}$$
$$=x^{-12}y^{-16}z^{-20}$$
When an exponent is negative, write the expression as a fraction and move the base from the numerator to the denominator (or vise versa) making the exponent positive.
$$=\frac{1}{x^{12}y^{16}z^{20}}$$
