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If the operation $ is defined such that x$y = x^y*y^x, what is the val

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If the operation $ is defined such that x$y = x^y*y^x, what is the val [#permalink]

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New post 06 Jan 2017, 03:08
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Re: If the operation $ is defined such that x$y = x^y*y^x, what is the val [#permalink]

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New post 06 Jan 2017, 07:31
Bunuel wrote:
If the operation $ is defined such that x$y = x^y*y^x, what is the value of 4$(1/2)?

A. 4
B. 2
C. 0.25
D. 0.125
E. 0.0625


x$y = x^y*y^x
=4^1/2 * (1/2)^4
=2*1/16
=1/8

Ans D
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Re: If the operation $ is defined such that x$y = x^y*y^x, what is the val [#permalink]

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New post 06 Jan 2017, 08:34
Bunuel wrote:
If the operation $ is defined such that x$y = x^y*y^x, what is the value of 4$(1/2)?

A. 4
B. 2
C. 0.25
D. 0.125
E. 0.0625


4$(1/2)

= \(4^{1/2}*(\frac{1}{2})^4\)

= \(2*(\frac{1}{2})^4\)

= \((1/2)^3\)

= \(\frac{1}{8}\)

= \(0.125\)

Hence, answer will be (D) 0.125
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Re: If the operation $ is defined such that x$y = x^y*y^x, what is the val [#permalink]

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New post 06 Jan 2017, 13:36
\(X $ Y = x^{y} y^{x}\)
$ = I thought it's a type of operation

4$(1/2) = \(4^{\frac{1}{2}}\) \(\frac{1}{2}^{4}\)
2 x \(\frac{1}{16}\)
D
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Re: If the operation $ is defined such that x$y = x^y*y^x, what is the val [#permalink]

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New post 09 Jan 2017, 10:46
Bunuel wrote:
If the operation $ is defined such that x$y = x^y*y^x, what is the value of 4$(1/2)?

A. 4
B. 2
C. 0.25
D. 0.125
E. 0.0625


We are given that the operation $ is defined such that x$y = (x^y)(y^x)

We need to determine the value of 4$(1/2). From the left side of the given pattern, we see that x = 4 and y = ½. Substituting these values into the expression on the right side of the given pattern, we obtain:

4^(1/2) x (1/2)^4

2 x 1/16 = 2/16 = 1/8 = 0.125

Answer: D
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Re: If the operation $ is defined such that x$y = x^y*y^x, what is the val [#permalink]

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New post 20 Feb 2017, 19:18
Okay so If the operation $ is defined such that x$y = x^y*y^x, what is the value of 4$(1/2)?

Therefore 4$(1/2)= 4^1/2 * 1/2^4
Instead of trying to calculate the answer by plugging in step by step, I tried to put myself in the shoes of Bunuel or Matt Damon
4^1/2 registered in my mind as 4 square root 2 and 1/2 to the 4th can be though of as 1^4/2^4 (learned that property from Kaplan) - automatically 2^4 = 16 ( memorized powers of 2) and of course fractions can just be multiply straightforward 2/1 times 1/16 equals 2/16 then reduce to 1/8
Re: If the operation $ is defined such that x$y = x^y*y^x, what is the val   [#permalink] 20 Feb 2017, 19:18
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If the operation $ is defined such that x$y = x^y*y^x, what is the val

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