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What is the value of 5^(1/5)*5^(2/5)*5^(3/5)*5^(4/5)

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What is the value of 5^(1/5)*5^(2/5)*5^(3/5)*5^(4/5)  [#permalink]

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New post Updated on: 11 Dec 2013, 07:02
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Difficulty:

  5% (low)

Question Stats:

85% (00:45) correct 15% (01:32) wrong based on 451 sessions

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What is the value of \(5^{\frac{1}{5}} * 5^{\frac{2}{5}} * 5^{\frac{3}{5}} * 5^{\frac{4}{5}}\) ?

A. \(\sqrt{5}\)
B. 5
C. \(5\sqrt{5}\)
D. 25
E. \(25\sqrt{5}\)

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Originally posted by greatchap on 22 Sep 2010, 07:14.
Last edited by Bunuel on 11 Dec 2013, 07:02, edited 2 times in total.
Renamed the topic, edited the question and added the OA.
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Re: Basic arithmetic  [#permalink]

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New post Updated on: 22 Sep 2010, 07:27
Apply this formula: \(X^a * X^b = X^(a+b)\)

here: expression comes to 5^1/5 + 2/5 + 3/5 + 4/5 = 5 ^ 10/5 = \(5^2\) = 25.

Originally posted by soumanag on 22 Sep 2010, 07:20.
Last edited by soumanag on 22 Sep 2010, 07:27, edited 1 time in total.
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Re: Basic arithmetic  [#permalink]

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New post 22 Sep 2010, 07:25
1
greatchap wrote:
Hi Guys,

Came across a basic arithmetic ques. How can I solve it ?

Q-1) What is the value of \(5^1/5 * 5^2/5 * 5^3/5 * 5^4/5\) ? (Here again) Image

I don't think the ans is 25 as I saw somewhere. ?

Thanks,

GR


Operations involving the same bases:

Keep the base, add or subtract the exponent (add for multiplication, subtract for division)
\(a^n*a^m=a^{n+m}\)

\(\frac{a^n}{a^m}=a^{n-m}\)

So, \(5^{\frac{1}{5}}*5^{\frac{2}{5}}*5^{\frac{3}{5}}*5^{\frac{4}{5}}=5^{\frac{1}{5}+\frac{2}{5}+\frac{3}{5}+\frac{4}{5}}=5^{\frac{10}{5}}=5^2=25\).

Hope it helps.
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Re: Basic arithmetic  [#permalink]

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New post 22 Sep 2010, 07:38
Thanks. I got it. It just slipped initially. I need to add the powers.
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Re: Basic arithmetic  [#permalink]

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New post 10 Oct 2013, 20:16
When the base is the same, just add the powers

SO, in this case, 5^ (1/5+2/5+3/5+4/5) = 5^2 = 25
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Re: What is the value of 5^(1/5)*5^(2/5)*5^(3/5)*5^(4/5)  [#permalink]

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New post 11 Dec 2013, 05:49
Can someone add answer choices so we can use the timer? would be great!
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Re: What is the value of 5^(1/5)*5^(2/5)*5^(3/5)*5^(4/5)  [#permalink]

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New post 11 Dec 2013, 07:02
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Re: What is the value of 5^(1/5)*5^(2/5)*5^(3/5)*5^(4/5)  [#permalink]

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New post 27 Aug 2018, 06:17
greatchap wrote:
What is the value of \(5^{\frac{1}{5}} * 5^{\frac{2}{5}} * 5^{\frac{3}{5}} * 5^{\frac{4}{5}}\) ?

A. \(\sqrt{5}\)
B. 5
C. \(5\sqrt{5}\)
D. 25
E. \(25\sqrt{5}\)

\(5^{\frac{1}{5}} * 5^{\frac{2}{5}} * 5^{\frac{3}{5}} * 5^{\frac{4}{5}}\)

Or, \(5^{\frac{1}{5}+\frac{2}{5}+\frac{3}{5}+\frac{4}{5}}\)

Or, \(5^{\frac{1+2+3+4}{5}}\)

Or, \(5^{\frac{10}{5}}\)

Or, \(5^2 = 25\), Answer must be (D)
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Re: What is the value of 5^(1/5)*5^(2/5)*5^(3/5)*5^(4/5) &nbs [#permalink] 27 Aug 2018, 06:17
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