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c^d=(1/c)^(3d-8) what is the value of c^d? a) c=4 b) d=

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c^d=(1/c)^(3d-8) what is the value of c^d? a) c=4 b) d= [#permalink] New post 05 Aug 2006, 20:21
c^d=(1/c)^(3d-8)
what is the value of c^d?
a) c=4
b) d= root(c)
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 [#permalink] New post 06 Aug 2006, 01:13
c^d=(1/c)^(3d-8)
So, c^d=(c^8)/(c^3d )
or, (c^d)*(c^3d)=c^8
or, c^(d+3d)=c^8
or c^4d = c^8
or 4d=8
so, d=2.

Now we need to find c^d or c^2.

A) If we know c=4, we can find the answer (4^2=16)
B) d= root(c), so, c = d^2, c=2^2 = 4, so we can find the answer.

Hence in my opinion the answer choice is D

Cheers.
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 [#permalink] New post 06 Aug 2006, 01:27
D

c^d=(1/c)^(3d-8) solve this first

c^d=(c^-1)^(3d-8)
c^d=(c)^(-3d+8)
i.e d = -3d+8
i.e d = 2

St1: we know both c and d. c^d = 4^2 = 16 : SUFF

St2: if d = 2 then c = 4. Hence c^d = 4^2 = 16: SUFF
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  [#permalink] 06 Aug 2006, 01:27
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