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Suppose y=2^x^2+2^x+3. Which of these x-values gives the s

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

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New post 16 Mar 2018, 00:56
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A
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C
D
E

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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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New post 16 Mar 2018, 01:20
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

Answer: option 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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New post 18 Mar 2018, 23:21
=>

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.
Answer : 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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New post 04 Apr 2018, 04:56
Could someone explain me why 2^(-3)^2 does not equal 2^(-6)?
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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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New post 04 Apr 2018, 05:35
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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