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# Square of a exponent with root

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Director
Joined: 07 Jun 2004
Posts: 610

Kudos [?]: 924 [0], given: 22

Location: PA
Square of a exponent with root [#permalink]

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17 Jul 2010, 16:33
what is

square of 5^sqrt(2) ?

in English it translates to what is

square of five to the power of square root of 2
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If the Q jogged your mind do Kudos me : )

Kudos [?]: 924 [0], given: 22

Kaplan GMAT Instructor
Joined: 21 Jun 2010
Posts: 146

Kudos [?]: 222 [0], given: 0

Location: Toronto
Re: Square of a exponent with root [#permalink]

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17 Jul 2010, 21:33
rxs0005 wrote:
what is

square of 5^sqrt(2) ?

in English it translates to what is

square of five to the power of square root of 2

Hi!

A fundamental rule of math is that, no matter how weird things look, the same basic rules always apply.

The basic exponent raised to an exponent rule is:

$$(x^a)^b = x^{a*b}$$

Applying the rule to your question:

$$(5^sqrt2)^2 = 5^{sqrt2 * 2} = 5^{2sqrt2}$$

Kudos [?]: 222 [0], given: 0

Re: Square of a exponent with root   [#permalink] 17 Jul 2010, 21:33
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