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Sub 505 Level|   Algebra|   Arithmetic|   Exponents|   Roots|      
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greatchap
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What is the value of 5^(1/5)*5^(2/5)*5^(3/5)*5^(4/5) Updated on: 11 Dec 2013, 08:02
Originally posted by greatchap on 22 Sep 2010, 08:14.
Last edited by Bunuel on 11 Dec 2013, 08:02, edited 2 times in total.
Renamed the topic, edited the question and added the OA.
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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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D

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What is the value of 5^(1/5)*5^(2/5)*5^(3/5)*5^(4/5) Updated on: 22 Sep 2010, 08:27
Originally posted by soumanag on 22 Sep 2010, 08:20.
Last edited by soumanag on 22 Sep 2010, 08:27, edited 1 time in total.
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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.
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What is the value of 5^(1/5)*5^(2/5)*5^(3/5)*5^(4/5) 22 Sep 2010, 08:25
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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)

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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What is the value of 5^(1/5)*5^(2/5)*5^(3/5)*5^(4/5) 22 Sep 2010, 08:38
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Thanks. I got it. It just slipped initially. I need to add the powers.
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What is the value of 5^(1/5)*5^(2/5)*5^(3/5)*5^(4/5) 10 Oct 2013, 21:16
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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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What is the value of 5^(1/5)*5^(2/5)*5^(3/5)*5^(4/5) 11 Dec 2013, 06:49
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Can someone add answer choices so we can use the timer? would be great!
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What is the value of 5^(1/5)*5^(2/5)*5^(3/5)*5^(4/5) 11 Dec 2013, 08:02
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Can someone add answer choices so we can use the timer? would be great!

Done. Thank you for the suggestion.
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What is the value of 5^(1/5)*5^(2/5)*5^(3/5)*5^(4/5) 27 Aug 2018, 07:17
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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. \(25\sqrt{5}\)
\(5^{\frac{1}{5}} * 5^{\frac{2}{5}} * 5^{\frac{3}{5}} * 5^{\frac{4}{5}}\)

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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What is the value of 5^(1/5)*5^(2/5)*5^(3/5)*5^(4/5) 22 Oct 2019, 11:03
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