# Solve for unknown in exponential equation

How do I solve for an unknown in the base of an exponential equation. In my example W is unknown: $$PPV=K\cdot\left(\frac{D}{W^{0.5}}\right)^{-1.6}$$

• Start with dividing both sides by $K$ and then raise both sides to the power $\dfrac{-1}{1.6}$ – David Peterson Aug 30 '16 at 6:00

$$PPV=K\cdot\left(\frac{D}{W^{0.5}}\right)^{-1.6} \implies \left(\frac{PPV}{K}\right)^{-5/8}\cdot \frac{1}{D}=\frac{1}{W^{.5}}.$$
Can you see how very mild manipulation will yield the answer? The idea here is to see how to express one variable ($W$) in terms of the rest.