If x 0, what is the value of (x^w/x^y)^4 ? (1) w = y

Ans: d)
As long as it is the powers of even number the answer is going to be 1.

My take is D.

Here is my explanation.

The equation in question stem can be simplfied as X^(4*(w-y)).

Clue 1: w = y ==> X ^ 0 = 1 We know the value of the expression in the question stem. Hence sufficient.

Clue 2: x^2 = 1 ==> X = +/-1 ==> 1 ^ even number = 1. ==> 1 ^ 2*2*(w-y) = 1. Again we know the value of the expression in the question stem. Hence sufficient.

Dear Bunuel, I want to ask what will be the value of (a/b)^- m/n equal to? Does it will be equal to (b/a)^n/m?

\((\frac{a}{b})^{-\frac{m}{n}}=\frac{1}{(\frac{a}{b})^{\frac{m}{n}}}=\)

\(=(\frac{1}{\frac{a}{b}})^{\frac{m}{n}}=(\frac{b}{a})^{\frac{m}{n}}\).

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hi ... irrespective of the value of x as 1 or -1... the value will be 1 since the entire has the power of an even number,4..

Hi All,

This DS question can be solved with a mix of Number Property Rules and TESTing VALUES:

We're told that X cannot = 0. We're asked for the value of [(X^W)/(X^Y)]^4

While this may look "scary", it's actually based on some basic math rules/patterns. Notice how the "base" of both the numerator AND the denominator are the SAME....that matters....

Fact 1: W = Y

Let's TEST VALUES:

IF...
X = 1
W = 1
Y = 1

[(1^1)/(1^1)]^4 = (1/1)^4 = 1

IF....
X = 2
W = 3
Y = 3

[(2^3)/(2^3)]^4 = (8/8)^4 = (1/1)^4 = 1

From this work, you should notice that the fraction ALWAYS equals 1, so the answer will ALWAYS be 1^4 = 1. That will always occur regardless of what you TEST for the 3 variables (in Fact 1).
Fact 1 is SUFFICIENT

Fact 2: X^2 = 1

This tells us that X = 1 OR X = -1

Here's where some Number Property knowledge comes in handy.

+1 raised to ANY power = 1, so (1^W) and (1^Y) BOTH always = 1......and 1/1 = 1.....so 1^4 = 1

-1 raised to an EVEN power = 1
-1 raised to an ODD power = -1

While this might appear to yield different answer, you must remember what the specific question asks for....

With these two restrictions on the numerator and denominator, we have 4 possible calculations (and 2 possible outcomes):

(+1)/(-1) = -1
(-1)/(+1) = -1
(+1)/(+1) = 1
(-1)/(-1) = 1

(-1)^4 = 1
(+1)^4 = 1

So the answer is the SAME regardless.
Fact 2 is SUFFICIENT.

Final Answer:

GMAT assassins aren't born, they're made,
Rich

What if the value of w-y =7/4??

in that case -1^4(w-y)

=-1^4(7/4)
= -1^7
=-1