Question

Given, $x^{-\frac{1}{2}}=\frac{1}{16}$
What is the value of $x$ in the equation above?

• A. $256$
• B. $4$
• C. $128$
• D. $2$

Answer 1

The correct option is A $256$

Given, $x^{-\frac{1}{2}}=\frac{1}{16}$
$\Rightarrow \frac{1}{{\left(x\right)}^{\frac{1}{2}}}=\frac{1}{16}$
$\Rightarrow \frac{1}{\sqrt{x}}=\frac{1}{16}$
$\Rightarrow \sqrt{x}=16$
On squaring both sides, we get
${\left(\sqrt{x}\right)}^2={16}^2$
$\Rightarrow x=256$