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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]  22 Sep 2010, 07:14
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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. $$25\sqrt{5}$$
[Reveal] Spoiler: OA

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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.
Manager
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Re: Basic arithmetic [#permalink]  22 Sep 2010, 07:20
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.

Last edited by soumanag on 22 Sep 2010, 07:27, edited 1 time in total.
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Re: Basic arithmetic [#permalink]  22 Sep 2010, 07:25
Expert's post
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)

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]  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]  10 Oct 2013, 10:11
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Re: Basic arithmetic [#permalink]  10 Oct 2013, 20:16
1
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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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Re: What is the value of 5^(1/5)*5^(2/5)*5^(3/5)*5^(4/5) [#permalink]  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]  11 Dec 2013, 07:02
Expert's post
unceldolan wrote:
Can someone add answer choices so we can use the timer? would be great!

Done. Thank you for the suggestion.
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Re: What is the value of 5^(1/5)*5^(2/5)*5^(3/5)*5^(4/5)   [#permalink] 11 Dec 2013, 07:02
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