Question

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Answer 1

Recall that
\[\sqrt a=c^{1/2}\]
and that
\[(a^b)^c=a^{bc}\]
This means you can write the right side of the equation as
\[\large\sqrt2^{4x+8}=\left(2^{1/2}\right)^{4x+8}=2^{\frac{4x+8}{2}}=2^{2x+4}\]
Does this make sense so far?

Answer 2

Good. So you have
\[\large8=2^{2x+4}\]
8 is the cube of 2, so you have
\[\large2^3=2^{2x+4}\]
The bases are both 2, so if the left is equal to the right that means the exponents are the same. This means you have
\[3=2x+4\]
Got it?

Answer 3

yw