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

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

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psarma: Junior | Next Rank: 30 Posts; Posts: 24; Joined: Wed Jun 29, 2011 1:47 am

Re: If $8^c\cdot \sqrt8=\dfrac{8^a}{8^b}$ then $a = ?$

by psarma » Thu Oct 01, 2020 3:40 pm

$8^c$ . $\sqrt{8}$ = $8^{\left(c+\frac{1}{\left(2\right)}\right)}$
Likewise, $8^a$ / $8^b$ = $8^{a-b}$
Thus, c+1/2=a-b
or a = b+c+1/2

Option E

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