If \(8^c\cdot \sqrt8=\dfrac{8^a}{8^b}\) then \(a = ?\)

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If \(8^c \cdot\sqrt8=\dfrac{8^a}{8^b}\) then \(a = ?\)

A. \(b\left(\dfrac12 + c\right)\)

B. \(\dfrac{bc}2\)

C. \(\dfrac{b + c}2\)

D. \(2b + c\)

E. \(\dfrac12 + b + c\)

Answer: E

Source: Magoosh

Junior | Next Rank: 30 Posts
Posts: 24
Joined: 29 Jun 2011
\(8^c\) . \(\sqrt{8}\) = \(8^{\left(c+\frac{1}{\left(2\right)}\right)}\)
Likewise, \(8^a\) / \(8^b\) = \(8^{a-b}\)
Thus, c+1/2=a-b
or a = b+c+1/2

Option E