Find the value of y given that 4^(y^2)/64 = 2^(-y) and y

Question

Find the value of y given that  \frac{4^{y^2}}{64}=2^{-y}  and  y < |y|

A. -4
B. -3
C. -2
D. -1
E. 2

Showmeyaa · Accepted Answer

\frac{2^{2y^2}}{2^6} = 2^{-y} 
 2y^2 - 6 = -y 
 2y^2 + 4y - 3y - 6 = 0 
 2y(y + 2) - 3(y + 2) = 0 
y =  \frac{3}{2} ; y = -2
Since, y < |y| y = -2

IMO, (C)!

Bunuel · Answer

This question is a part of  Are You Up For the Challenge: 700 Level Questions  collection.

nermeendhuca · Answer

I don't get it. If I plug in y=-2 it doesn't work...

y^2/16 = 2^-y

plug in y=-2

4/16 = 4
... 1/4= 4 <-- not equal

What am I doing wrong?

mintchoco · Answer

I used to have the same thought as you, but giving the equation a second look has enabled me to know what my fault was

It's 4 to the power of y to the power of 2 (4^y^2), not 4 times y^2 (4y^2). I had the wrong answer as I see things in the former way. (C) is the correct answer.

tinamar · Answer

When raising an exponential term to an exponent, you can multiply the exponents but how come in this case, if we do that, we get a different answer? For example, why can't 4^(y^2 ) be simplified to 4^(2y)?

Nabneet · Answer

Operations involving the same exponents: Keep the exponent, multiply or divide the bases a^n*b^n=(ab)^n \frac{a^n}{b^n}=(\frac{a}{b})^n (a^m)^n=a^{mn} a^{m^n}=a^{(m^n)} and not (a^m)^n Check the thread: https://gmatclub.com/forum/exponents-an ... 74993.html

Find the value of y given that 4^(y^2)/64 = 2^(-y) and y < |y|

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