a: \(A=\dfrac{x^5}{x^3}\cdot\dfrac{y^{-2}}{y}=x^2\cdot y^{-1}=\dfrac{x^2}{y}\)

b: \(B=\dfrac{x^2\cdot y^{-3}}{x^3\cdot y^{-12}}=\dfrac{x^2}{x^3}\cdot\dfrac{y^{-3}}{y^{-12}}=\dfrac{1}{x}\cdot y^{-3+12}=\dfrac{y^9}{x}\)

a) \(A=\dfrac{x^5y^{-2}}{x^3y}=\dfrac{x^5}{x^3}.\dfrac{1}{y^{2-1}}=x^{5-3}y^{-1}=x^2y^{-1}\).

b) \(B=\dfrac{x^2y^{-3}}{\left(x^{-1}y^4\right)^{-3}}=\dfrac{x^2y^{-3}}{x^3y^{-12}}=x^{2-3}y^{-3-\left(-12\right)}=\dfrac{1}{xy^9}\)

a) \(\sqrt{\dfrac{x-2\sqrt{x}+1}{x+2\sqrt{x}+1}}\sqrt{\dfrac{\left(\sqrt{x+1}\right)^2}{\left(\sqrt{x}+1\right)^2}}\)

=\(\dfrac{\sqrt{x}-1}{\sqrt{x}+1};x\ge0\)

b) Ta có: \(\dfrac{x-1}{\sqrt{y}-1}\cdot\sqrt{\dfrac{\left(y-2\sqrt{y}+1\right)^2}{\left(x-1\right)^4}}\)

\(=\dfrac{x-1}{\sqrt{y}-1}\cdot\dfrac{\sqrt{y}-1}{\left(x-1\right)^2}\)

\(=\dfrac{1}{x-1}\)

a) \(x^2+y^2\)

b) \(\dfrac{\left(x-y\right)^3}{x+y}\)

(Vì x > 0 nên |x| = x; y2 > 0 với mọi y ≠ 0)

(Vì x2 ≥ 0 với mọi x; và vì y < 0 nên |2y| = – 2y)

(Vì x < 0 nên |5x| = – 5x; y > 0 nên |y3| = y3)

(Vì x2y4 = (xy2)2 > 0 với mọi x ≠ 0, y ≠ 0)

a) 1/y 

b) - x^2 y 

c) -25x^2 / y^2

d) 4x/5y

yx.x2y4=yx.x2y4=yx.|x||y2|=yx.xy2=1y.

(Do $x>0$ nên $|x|=x$, $y\ne 0$ $\Rightarrow$ $y^2>0$ nên $|y^2|=y^2$)

x44y2=2y2.x44y2=2y2.|x2||2y|=2y2.x2−2y=2y2.x2−2y=−x2y.

(Do $y<0$ nên $|2y|=-2y$ và $x^2\ge 0$ nên $|x^2|=x^2$)

25x2y6=5xy.25x2y6=5xy.|5x||y3|=5xy.−5xy3=5xy.(−5x)y3=−25x2y2.

(Do $x<0$ nên $|5x|=-5x$ và $y>0$ $\Rightarrow$ $y^3>0$ nên $|y^3|=y^3$)

16x4y8=0,2x3y3.16x4y8=210.x3y3.4|x2y4|=15.x3y3.4x2y4=4x3y35x2y4=4x5y.

( Do $x\ne 0$ $\Rightarrow$ $x^2>0$ và