Question

For all $x\ne 0$, simplify $\frac{5}{\left(\frac{1}{x^2}\right)}$.

• A. $5x^{-2}$
• B. $5x^2$
• C. $\frac{x^2}{5}$
• D. $\frac{5}{x^2}$
• E. $25x^2$

Answer 1

The correct option is B $5x^2$

We know that $\frac{1}{x^2}=x^{-2}$

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

$\Rightarrow \frac{5}{\left(\frac{1}{x^2}\right)}=5x^2$