When you're dealing with exponent questions, it's usually helpful to get things to look as alike as possible. For this problem, remember that roots are just exponents: a square root is the same as the $\frac{1}{2}$ power.

So first, rewrite the equation: $8^c * 8^\frac{1}{2}$ = $\frac{8^a}{8^b}$

Next, let's get rid of the denominator by multiplying both sides by $8^b$

$8^b*8^c*8^\frac{1}{2} = 8^a$

Next, apply the power rules. When multiplying numbers with the same base, you can add the powers:

$8^b*8^c*8^\frac{1}{2} = 8^{(b+c+1/2)}$=$8^a$

Now, since the base is the same on both sides, just ignore it. $b+c+\frac{1}{2}$ = a.

Answer: E

Remember n^1/2 = square root of n

8^c * 8^1/2 = 8^a / 8^b

Isolate the exponents and solve for a:
c + 1/2 = a - b
c + b + 1/2 = a
Answer is E.