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Math Revolution GMAT Instructor V
Joined: 16 Aug 2015
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GMAT 1: 760 Q51 V42 GPA: 3.82
Suppose y=2^x^2+2^x+3. Which of these x-values gives the s  [#permalink]

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Difficulty:   25% (medium)

Question Stats: 76% (01:24) correct 24% (01:34) wrong based on 112 sessions

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[GMAT math practice question]

Suppose $$y=2^{x^2}+2^{x+3}$$. Which of these $$x$$-values gives the smallest value of $$y$$?

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

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Re: Suppose y=2^x^2+2^x+3. Which of these x-values gives the s  [#permalink]

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MathRevolution wrote:
[GMAT math practice question]

Suppose $$y=2^{x^2}+2^{x+3}$$. Which of these $$x$$-values gives the smallest value of $$y$$?

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

A. -3 y = 2^9 + 2^0 = 513
B. -2 y = 2^4 + 2^1 = 17
C. -1 y = 2^1 + 2^2 = 5
D. 1 y = 2^1 + 2^4 = 18
E. 2 y = 2^4 + 2^5 = 48

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Math Revolution GMAT Instructor V
Joined: 16 Aug 2015
Posts: 8005
GMAT 1: 760 Q51 V42 GPA: 3.82
Re: Suppose y=2^x^2+2^x+3. Which of these x-values gives the s  [#permalink]

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=>

Since the exponent function $$y=2^x$$ is an increasing function, the smallest value of $$x^2+2x+3$$ gives the smallest value of $$y=2^{x^2}+2^{x+3}$$.
Since $$x^2+2x+3 = (x+1)^2 + 2$$, the exponent $$(x+1)^2 + 2$$ has a minimum value when $$x = -1$$.

Therefore, the answer is C.
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Re: Suppose y=2^x^2+2^x+3. Which of these x-values gives the s  [#permalink]

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Could someone explain me why 2^(-3)^2 does not equal 2^(-6)?
Math Expert V
Joined: 02 Sep 2009
Posts: 58324
Re: Suppose y=2^x^2+2^x+3. Which of these x-values gives the s  [#permalink]

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PedroBodnar wrote:
Could someone explain me why 2^(-3)^2 does not equal 2^(-6)?

$$a^m^n=a^{(m^n)}$$ and not $$(a^m)^n$$ (if exponentiation is indicated by stacked symbols, the rule is to work from the top down). Thus, $$2^{(-3)^2}=2^{((-3)^2)}=2^9$$ and not $$(2^{(-3)})^2=2^{-6}$$

On the other hand, $$(a^m)^n=a^{mn}$$.

8. Exponents and Roots of Numbers

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_________________ Re: Suppose y=2^x^2+2^x+3. Which of these x-values gives the s   [#permalink] 04 Apr 2018, 05:35
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Suppose y=2^x^2+2^x+3. Which of these x-values gives the s

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