What is $h(2)-h(4)$, given that $h(x)=2^x$?

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Evluate $h(2)$ and $h(4)$.

$$h(x)=2^x$$ $$h(2)=2^2 = 4$$ $$h(4)=2^4 = 16$$

Accordingly,

$$h(2)-h(4)$$ $$=4-16$$ $$= \boxed{-12}$$