Bài làm:
a) Vì x < 0 và y > 0, ta có:
5xy . $\sqrt[]{\frac{25x^2}{y^6}}$ = 5xy. $\sqrt[]{\frac{(5x)^2}{(y^3)^2}}$
= 5xy . $\frac{|5x|}{|y^3|}$ = 5xy . $\frac{-5x}{y^3}$ = $\frac{-25x^2}{y^2}$
b) Vì a<0 và b $\neq$ 0
⇒ ab . $\sqrt[]{\frac{3}{a^2b^4}}$ = ab.$\sqrt[]{\frac{3}{(ab^2)^2}}$
= ab . $\frac{\sqrt[]{3}}{|ab^2|}$ = ab. $\frac{\sqrt[]{3}}{-ab^2}$ = $\frac{-\sqrt[]{3}}{b}$
c) Vì a ≥ 0
⇒ $\sqrt[]{\frac{2a}{3}}$ . $\sqrt[]{\frac{3a}{8}}$ = $\sqrt[]{\frac{2a}{3}.\frac{3a}{8}}$
= $\sqrt[]{\frac{a^2}{4}}$ = $\sqrt[]{(\frac{a}{2})^2}$ = |$\frac{a}{2}$ | = $\frac{a}{2}$
d) Vì a > 1
⇒ $\sqrt[]{27.48.(1-a)^2}$ = $\sqrt[]{3^3.3.16.(1-a)^2}$
= $\sqrt[]{3^4.4^2.(1-a)^2}$ = $\sqrt[]{[3^2.4.(1-a)]^2}$
= | 3² . 4 . (1-a)| = 36|1-a| = 36(a-1) = 36a - 36
