Question Bank › General Aptitude › Surds and Indices › ABC26GN1974ABC26GN1974 · Surds and Indices Subject: General Aptitude · Chapter: Surds and Indices · Exam: · Marks: · Difficulty:
The expression $\frac{\left(x+\frac{1}{y}\right)^{a} \cdot\left(x-\frac{1}{y}\right)^{b}}{\left(y+\frac{1}{x}\right)^{a} \cdot\left(y-\frac{1}{x}\right)^{b}}$ reduces to
(a) $\left(\frac{x}{y}\right)^{a-b}$
(b) $\left(\frac{y}{x}\right)^{a-b}$
(c) $\left(\frac{x}{y}\right)^{a+b}$
(d) $\left(\frac{y}{x}\right)^{a+b}$
Answer Explanation Given Exp. $=\frac{\left(\frac{x y+1}{y}\right)^{a} \cdot\left(\frac{x y-1}{y}\right)^{b}}{\left(\frac{x y+1}{x}\right)^{a} \cdot\left(\frac{x y-1}{x}\right)^{b}}$ $$\begin{aligned} & =\frac{(x y+1)^{a} \cdot(x y-1)^{b} \cdot x^{a} \cdot x^{b}}{(x y+1)^{a} \cdot(x y-1)^{b} \cdot y^{a} \cdot y^{b}} \\ & =\frac{x^{a+b}}{y^{a+b}}=\left(\frac{x}{y}\right)^{a+b} . \end{aligned}$$
Explanation as extracted from the printed page; notation may be imperfect.
← Previous in chapter · Chapter list · Next in chapter → Open in whiteboard · Browse this chapter in the app