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5^(x-1)/5^(-1-2x) is equal to which of the following?

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5^(x-1)/5^(-1-2x) is equal to which of the following?  [#permalink]

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New post Updated on: 20 Oct 2016, 07:27
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\(\frac{5^{x-1}}{5^{-1-2x}}\) is equal to which of the following?

A. 5^(x-1)
B. 5^(1-x)
C. 25^2x
D. 25^-2x
E. 125^x

* A solution will be posted in 2 days.

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Originally posted by MathRevolution on 19 Oct 2016, 23:43.
Last edited by Abhishek009 on 20 Oct 2016, 07:27, edited 1 time in total.
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5^(x-1)/5^(-1-2x) is equal to which of the following?  [#permalink]

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New post 20 Oct 2016, 06:18
MathRevolution wrote:
5^(x-1)/5^(-1-2x) is equal to which of the following?

A. 5^(x-1)
B. 5^(1-x)
C. 25^2x
D. 25^-2x
E. 125^x

* A solution will be posted in 2 days.


\(5^(x-1)/5^(-1-2x)\) = \(5^(x-1) * 5^(1+2x)\) = \(5^(3x)\) = \(125^x\)

Hence, E
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Re: 5^(x-1)/5^(-1-2x) is equal to which of the following?  [#permalink]

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New post 20 Oct 2016, 07:30
MathRevolution wrote:
\(\frac{5^{x-1}}{5^{-1-2x}}\) is equal to which of the following?

A. 5^(x-1)
B. 5^(1-x)
C. 25^2x
D. 25^-2x
E. 125^x

* A solution will be posted in 2 days.


\(\frac{5^{x-1}}{5^{-1-2x}}\) = \(5^{(x-1) - ( -1-2x ) }\) = \(5^{x-1 +1 + 2x ) }\) = \(5^{3x}\) = \(125^x\)

Answer will be (E)

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Re: 5^(x-1)/5^(-1-2x) is equal to which of the following?  [#permalink]

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New post 24 Oct 2016, 01:16
==>5^(x-1)/5^(-1-2x)=5^{x-1-(-1-2x)} = 5^(x-1+1+2x)=5^3x=(5^3)x=125^x.
E is the answer.
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Re: 5^(x-1)/5^(-1-2x) is equal to which of the following?  [#permalink]

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New post 25 Oct 2016, 20:10
I got the answer right but could someone explain why 25^2x isn't the right answer?

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Re: 5^(x-1)/5^(-1-2x) is equal to which of the following?  [#permalink]

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New post 26 Oct 2016, 22:00
gillyelephant wrote:
I got the answer right but could someone explain why 25^2x isn't the right answer?

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Hi gillyelephant,

==> 5x-1/5-1-2x =5x-1-(-1-2x) = 5x-1+1+2x=53x=(53)x=125x
no 25^2x=(25^2)^x=625^x.

Hope it helps.
Thank you.
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Re: 5^(x-1)/5^(-1-2x) is equal to which of the following?  [#permalink]

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New post 21 Mar 2018, 02:48
MathRevolution wrote:
\(\frac{5^{x-1}}{5^{-1-2x}}\) is equal to which of the following?

A. 5^(x-1)
B. 5^(1-x)
C. 25^2x
D. 25^-2x
E. 125^x

* A solution will be posted in 2 days.


\(\frac{5^{x-1}}{5^{-1-2x}}\)

\(\frac{5^x * 5^-1}{5^-1* 5^{-2x}}\)

It can be written as,

\(5^x * 5^{2x}\)

\(5^{3x}\)

\(125^x\)

(E)
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Re: 5^(x-1)/5^(-1-2x) is equal to which of the following?   [#permalink] 21 Mar 2018, 02:48
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