# Expressing a power

Express e in terms of c and d if $$2^{c}4^{d} = 8^{e}$$

Can someone give me step by step advice on how to answer this?

HallsofIvy
Homework Helper
Express e in terms of c and d if $$2^{c}4^{d} = 8^{e}$$

Can someone give me step by step advice on how to answer this?
4= 22 so 4d= (22)d= 22d. 8= 23 so 8e= (23)e= 23e.

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I dont get

$$(2^{3})^{e}= 3^{3e}$$

I see that 2³ = 8 and $$(^{e})^{3}$$ is $$^{3e}$$, but how can that be $$3^{3e}$$
?

P.S Can i ask, the dot in the middle of a line, is it suppost to represent a new equaion?

HallsofIvy