If x = y, which of the following could be equal to

Question

If  \sqrt{x}=y,  which of the following could be equal to  \frac{1}{(x^{−2})^{−2}}

A.  y^{-8} 
B.  y^{-4} 
C.  y^{-2} 
D.  y 
E.  y^2

Thanks,
Saquib
Quant Expert
e-GMAT

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HKD1710 · Answer

\sqrt{x}  = y --- we can now square both side

x = y^2  --- square two more times on both sides

x^4 = y^8

\frac{1}{(x^{−2})^{−2}}  =  \frac{1}{x^{4}}  =  \frac{1}{y^{8}}  =  y^{-8}

A

sashiim20 · Answer

\sqrt{x}=y, 
Squaring both sides; x =  y^2

\frac{1}{(x^{−2})^{−2}}  =  \frac{1}{(x^{4})}

Putting value of x in the fraction;  \frac{1}{(x^{4})}

\frac{1}{(y^2)^{4}}  =  \frac{1}{y^{8}}  =  y^{-8} 
Answer A...

EgmatQuantExpert · Answer

Official Solution Given : • \sqrt{x}=y Working Out : • \frac{1}{(x^{−2})^{−2}} • \frac{1}{x^4} It is given that • \sqrt{x}=y Taking 8th power on both sides we get: • x^4 = y^8 Therefore, • \frac{1}{x^4} =\frac{1}{y^8} =y^{-8} Correct Answer: Option A Thanks, Saquib Quant Expert e-GMAT Register for our Free Session on Number Properties (held every 3rd week) to solve exciting 700+ Level Questions in a classroom environment under the real-time guidance of our Experts

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generis · Answer

Pick nice numbers, and y is positive. When the principal square root symbol is written in the problem, we need to consider the positive square root only.

\sqrt{x}=y , and  \sqrt{4}= 2 ,  so x = 4 and y = 2

\frac{1}{(x^{−2})^{−2}}   =  \frac{1}{x^4}  ---> substitute 4 for x

=  \frac{1}{4^4}

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

=  \frac{1}{2^8}

=  2^{-8}

Substitute y for 2 --->  y^{-8}

Answer A

Shorten the math:  \frac{1}{4^4}  =  \frac{1}{256} , and  \frac{1}{256}  =  \frac{1}{2^8} , which is  2^{-8} . Substitute y for 2 --->  y^{-8}

Abhishek009 · Answer

\sqrt{x}=y,

Or,  x = y^2

\frac{1}{(x^{−2})^{−2}}

=  \frac{1}{(x^{−4})}

=  x^4

=  y^{2*4}

=  y^{8}

Hence, answer will be (A)  y^{8}

ehsan090 · Answer

I consider it very easy EGMAT is rarely kind for students
Answer:A
Time consumed:0:50(I cross check since was in doubt of EGMAT kindness)
√x=y
x^1/2=y
we have to make it x^4
So x^1/2*8=y^8
Multiply both sides with 8
Sp,
X^4=y^8
Since
1/(x^-2)^-2
1/x^4
put equivalent of x^4
it is
1/y^8
which is
y^-8

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If x = y, which of the following could be equal to

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