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# The operation is defined for all non-zero x and y by the equation x

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SVP
Status: Preparing GMAT
Joined: 02 Nov 2016
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The operation is defined for all non-zero x and y by the equation x  [#permalink]

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19 May 2017, 12:04
1
00:00

Difficulty:

25% (medium)

Question Stats:

71% (01:05) correct 29% (00:52) wrong based on 25 sessions

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The operation @ is defined for all non-zero x and y by the equation x@ y = x^y . Then the expression (x@ y)@ z is equal to

(A) x^y^z
(B) xyz
(C) (xy)^z
(D) (x^y) z
(E) (x^y)^z

Source: Nova GMAT

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Re: The operation is defined for all non-zero x and y by the equation x  [#permalink]

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19 May 2017, 13:15
The operation @ is defined for all non-zero x and y by the equation x@ y = x^y . Then the expression (x@ y)@ z is equal to

(A) x^y^z
(B) xyz
(C) (xy)^z
(D) (x^y) z
(E) (x^y)^z

Source: Nova GMAT

Sorry for the extra brackets. The "at" symbol used makes formatting hard; I can't figure out how to make it stop turning all that follows the symbol into a URL.

x @ y = $$x^y$$, which is the new LHS ==>

[$$x^y$$ @ z] is $$x^y$$ to the $${z}^th$$ power, which is

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Re: The operation is defined for all non-zero x and y by the equation x  [#permalink]

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19 May 2017, 21:46
I will try to solve this using smart numbers. I will avoid using values of 1, -1, 0 as more than one options are likely to yield the same answers if I take such values here.

lets take x=2, y=3, z=2.
Now x@y = 2^3 =8
and (x@y)@z = 8@2 = 8^2 = 64

Now we have to look at an option which gives us 64.

1) x^y^z = 2^3^2 = 2^9 =512
2) xyz = 2*3*2 =12
3) (xy)^z = (2*3)^2 = 6^2 =36
4) (x^y)z = (2^3)*2 = 8*2 =16
5) (x^y)^z = (2^3)^2 = 8^2 = 64

Re: The operation is defined for all non-zero x and y by the equation x &nbs [#permalink] 19 May 2017, 21:46
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