Question

If $y$ be the reciprocal of $x$, then the reciprocal of $y^2$ in terms of $x$ will be ____

Answer 1

Evaluate the Reciprocal:

We know that for reciprocal of any number,

$a=\frac{1}{a}$

Therefore, it is given that $y$ be the reciprocal of $x$,

$y=\frac{1}{x}$

Therefore $y^2$ in terms of $x$ will be,

$y^2={\left(\frac{1}{x}\right)}^2$

$=\frac{1}{x^2}$

Therefore, the reciprocal of $y^2=\frac{1}{{\displaystyle \frac{1}{x^2}}}$

$=x^2$

Hence, the required answer is $x^2$.