Answer
$d=\dfrac{k^2}{F^2}$
Work Step by Step
$\bf{\text{Solution Outline:}}$
To solve the given equation, $
F=\dfrac{k}{\sqrt{d}}
,$ in terms of $
h
,$ square both sides. Then use the laws of exponents and the properties of equality to isolate the variable.
$\bf{\text{Solution Details:}}$
Squaring both sides, the equation above is equivalent to
\begin{array}{l}\require{cancel}
(F)^2=\left(\dfrac{k}{\sqrt{d}}\right)^2
\\\\
F^2=\left(\dfrac{k}{\sqrt{d}}\right)^2
.\end{array}
Using the extended Power Rule of the laws of exponents which states that $\left( \dfrac{x^m}{z^p} \right)^q=\dfrac{x^{mq}}{z^{pq}},$ the equation above is equivalent to
\begin{array}{l}\require{cancel}
F^2=\dfrac{(k)^2}{(\sqrt{d})^2}
\\\\
F^2=\dfrac{k^2}{d}
.\end{array}
Using the properties of equality, the equation above is equivalent to
\begin{array}{l}\require{cancel}
d(F^2)=\left(\dfrac{k^2}{d}\right)d
\\\\
dF^2=k^2
\\\\
d=\dfrac{k^2}{F^2}
.\end{array}
