If b^(-1/2) = 4, what is the value of b?

Sep 4, 2015

You first rewrite the equation.

Explanation:

The $-$ in a power means it is 1 divided by.
$\frac{1}{2}$ as a power means sqrt

So ${b}^{- \frac{1}{2}}$ means $\frac{1}{\sqrt{b}}$

$\frac{1}{\sqrt{b}} = 4 \to 4 \cdot \sqrt{b} = 1 \to \sqrt{b} = \frac{1}{4} \to$

Square both sides:
${\sqrt{b}}^{2} = {\left(\frac{1}{4}\right)}^{2} \to b = \frac{1}{16}$

${\left(\frac{1}{16}\right)}^{-} 1 = \frac{1}{\frac{1}{16}} = 16 \to$
${16}^{\frac{1}{2}} = \sqrt{16} = 4$