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# If 8^c∗√8 = 8^a/8^b then a = ?

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Math Expert
Joined: 02 Sep 2009
Posts: 53063
If 8^c∗√8 = 8^a/8^b then a = ?  [#permalink]

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18 Oct 2018, 00:30
00:00

Difficulty:

25% (medium)

Question Stats:

73% (01:33) correct 27% (01:40) wrong based on 84 sessions

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If $$8^c∗\sqrt{8} = \frac{8^a}{8^b}$$ then a = ?

A. b(1/2 + c)

B. bc/2

C. (b + c)/2

D. 2b + c

E. 1/2 + b + c

_________________
Math Expert
Joined: 02 Aug 2009
Posts: 7334
Re: If 8^c∗√8 = 8^a/8^b then a = ?  [#permalink]

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18 Oct 2018, 02:43
Bunuel wrote:
If $$8^c∗\sqrt{8} = \frac{8^a}{8^b}$$ then a = ?

A. b(1/2 + c)

B. bc/2

C. (b + c)/2

D. 2b + c

E. 1/2 + b + c

Get all to power of 8
$$8^c∗\sqrt{8} = \frac{8^a}{8^b}.......8^c*8^{\frac{1}{2}}=\frac{8^a}{8^b}.........8^{c+\frac{1}{2}}=8^{a-b}... c+\frac{1}{2}=a-b.......a=b+c+\frac{1}{2}$$

OR

Make left side as 8, so let c=1/2 therefore If $$\sqrt{8}*\sqrt{8} = \frac{8^a}{8^b}......8^a=8*8^b.....a=b+1$$
Check for choices that give you a=b+1

A. b(1/2 + c)......b(1/2+1/2)=b...no

B. bc/2.....b*1/4....no

C. (b + c)/2.....(b+1/2)/2.....no

D. 2b + c......2b+1/2.....no

E. 1/2 + b + c....1/2+b+1/2=b+1

E
_________________

1) Absolute modulus : http://gmatclub.com/forum/absolute-modulus-a-better-understanding-210849.html#p1622372
2)Combination of similar and dissimilar things : http://gmatclub.com/forum/topic215915.html
3) effects of arithmetic operations : https://gmatclub.com/forum/effects-of-arithmetic-operations-on-fractions-269413.html
4) Base while finding % increase and % decrease : https://gmatclub.com/forum/percentage-increase-decrease-what-should-be-the-denominator-287528.html

GMAT Expert

Re: If 8^c∗√8 = 8^a/8^b then a = ?   [#permalink] 18 Oct 2018, 02:43
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