Question

The value of $\frac{{(x+\frac{1}{y})}^a{(x-\frac{1}{y})}^b}{{(y+\frac{1}{x})}^a{(y-\frac{1}{x})}^b}$ is equal to

• A. ${\left(\frac{x}{y}\right)}^{a+b}$
• B. ${\left(\frac{y}{x}\right)}^{a+b}$
• C. $(xy{)}^{a+b}$
• D. $\frac{x^n}{y^b}$

Answer 1

The correct option is A ${\left(\frac{x}{y}\right)}^{a+b}$

$Thegivenexpressionis\frac{{(x+\frac{1}{y})}^a{(x-\frac{1}{y})}^b}{{(y+\frac{1}{x})}^a{(y-\frac{1}{x})}^b}=\frac{{\left(\frac{xy+1}{y}\right)}^a{\left(\frac{xy-1}{y}\right)}^b}{{\left(\frac{xy+1}{x}\right)}^a{\left(\frac{xy-y}{x}\right)}^b}={\left(\frac{x}{y}\right)}^a{\left(\frac{x}{y}\right)}^b={\left(\frac{x}{y}\right)}^{a+b}\left(Ans\right)$