Q) If 3^6k = 8100 , (3^(k-1))^3 = ? Sorry for the

Question

Q) If 3^6k = 8100 , (3^(k-1))^3 = ? 

Sorry for the inconvenience of using too many ^s. But the question is simple though I am struggling.. 

If you can read and understand it, would you please help me to understand how to get the solution??

walker · Answer

(3^(k-1))^3=(3^3k)*(3^(-3))=root((3^6k))*(3^(-3))=root(8100)*1/27=90/27=10/3

pmenon · Answer

i follow everything until the second equal sign. Why are you equating the two expressions ?

walker · Answer

If I understand you right I'm not equating. 
do you ask me about (3^3k)=root(3^6k) ?
I made this to put 3^6k from the equation into the expression without knowing k.

GMAT TIGER · Answer

so smoth like your biking.

tarek99 · Answer

(3^(k-1))^3=(3^3k)*(3^(-3))= root((3^6k))*( 3^(-3))=root(8100)*1/27=90/27=10

walker, i like the fact that you managed to solve this without even looking for K, and that can help save time. However, I don't understand the area that i've bolded. Why did you root that expression? maybe I don't understand the rules and so would need your input, but I don't see how root(3^6k) can equal to 3^3k. would you please explain? thanks

walker · Answer

Thanks Tiger! I really like race! but sometimes it was not so smooth as equations :-D

walker · Answer

m^n=m^(n*2*1/2)=(m^(2*n))^1/2
or general rule: x^(n*m)=(x^n)^m=(x^m)^n

for example,

16=2^4=2^(4*2*1/2)=2^(8*1/2)=(2^8)^1/2=root(2^8)=root(256)=16

is it ok?

GK_Gmat · Answer

That is one sweet solution. I was wasting time trying to find the value of k.

tarek99 · Answer

wow, i'm amazed! thanks a lot for the explanation walker. this approach is really something!

Q) If 3^6k = 8100 , (3^(k-1))^3 = ? Sorry for the

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