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

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Re: Find the value of y given that 4^(y^2)/64 = 2^(-y) and y < |y| [#permalink]
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?
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Re: Find the value of y given that 4^(y^2)/64 = 2^(-y) and y < |y| [#permalink]
nermeendhuca wrote:
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?

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.
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Re: Find the value of y given that 4^(y^2)/64 = 2^(-y) and y < |y| [#permalink]
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)?
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Find the value of y given that 4^(y^2)/64 = 2^(-y) and y < |y| [#permalink]
tinamar wrote:
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)?

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| [#permalink]
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