Answer
a) $\frac{x^{10}}{yz^{4}}$
b) $r^{9}$$s^{2}$
Work Step by Step
a) $($$\frac{x^4z^2}{4y^5}$$)$$($$\frac{2x^3y^2}{z^3}$$)$$^2$ = $($$\frac{x^4z^2}{4y^5}$$)$$\frac{2^2x^{(3)(2)}y^{(2)(2)}}{z^{(3)(2)}}$ = $($$\frac{x^4z^2}{4y^5}$$)$$\frac{4x^{6}y^{4}}{z^{6}}$ = $x^{4+6}$$y^{4-5}$$z^{2-6}$ = $x^{10}$$y^{-1}$$z^{-4}$ = $\frac{x^{10}}{yz^{4}}$
We note that the 4 on top on the fraction and on the bottom
simplify to a times 1.
b) $\frac{(rs^2)^3}{(r^{-3}s^2)^2}$ = $\frac{r^3s^{(2)(3)}}{r^{(-3)(2)}s^{(2)(2)}}$ = $r^{3+6}$$s^{6-4}$ = $r^{9}$$s^{2}$
