Answer
$x^{12}y^6$
Work Step by Step
To solve $(\frac{x^4}{y^{-2}})^3$,
RECALL:
(i) The quotients-to-powers rule states that: $(\frac{a}{b})^n=\frac{a^n}{b^n}$
(ii) The power-rule states that $(a^m)^n=a^{mn}$
(iii) The negative-exponent rule states that: $a^{−m} =\frac{1}{a^m}$ and $\frac{1}{a^{-m}} = a^{m}$
Hence, using quotients-to-powers rule and power rule:
$(\frac{x^4}{y^{-2}})^3$ = $\frac{(x^{4})^3}{(y^{-2})^{3}}$
Using the power rule:
$=\frac{x^{4\times3}}{y^{-2\times3}}$
$=\frac{x^{12}}{y^{-6}}$
Using negative-exponent rule,
$=\frac{x^{12}}{y^{-6}} = x^{12}y^6$
