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# Which of the following expressions is equivalent to (s^2 + 9)^(-1/2) ?

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Math Expert
Joined: 02 Sep 2009
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Which of the following expressions is equivalent to (s^2 + 9)^(-1/2) ? [#permalink]

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22 Mar 2018, 23:43
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Which of the following expressions is equivalent to $$(s^2 + 9)^{(-\frac{1}{2})}$$ ?

A. $$-\frac{s^2 + 9}{2}$$

B. $$-\frac{1}{\sqrt{s^2 + 9}}$$

C. $$-\sqrt{s^2 + 9}$$

D. $$\frac{1}{s+3}$$

E. $$\frac{1}{\sqrt{s^2 + 9}}$$
[Reveal] Spoiler: OA

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Which of the following expressions is equivalent to (s^2 + 9)^(-1/2) ? [#permalink]

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23 Mar 2018, 00:19
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Bunuel wrote:
Which of the following expressions is equivalent to $$(s^2 + 9)^{(-\frac{1}{2})}$$ ?

A. $$-\frac{s^2 + 9}{2}$$

B. $$-\frac{1}{\sqrt{s^2 + 9}}$$

C. $$-\sqrt{s^2 + 9}$$

D. $$\frac{1}{s+3}$$

E. $$\frac{1}{\sqrt{s^2 + 9}}$$

As the calculation we're asked to do is straightforward, we'll just do it.
This is a Precise approach.

A negative power of a number is the reciprocal of that number to the positive power.
A power of 1/2 is the same as a square root. So:
So, $$(s^2 + 9)^{(-\frac{1}{2})} = \frac{1}{(s^2 + 9)^{\frac{1}{2}}}$$ = $$\frac{1}{\sqrt{s^2 + 9}}$$

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Re: Which of the following expressions is equivalent to (s^2 + 9)^(-1/2) ? [#permalink]

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23 Mar 2018, 00:30
Bunuel wrote:
Which of the following expressions is equivalent to $$(s^2 + 9)^{(-\frac{1}{2})}$$ ?

A. $$-\frac{s^2 + 9}{2}$$

B. $$-\frac{1}{\sqrt{s^2 + 9}}$$

C. $$-\sqrt{s^2 + 9}$$

D. $$\frac{1}{s+3}$$

E. $$\frac{1}{\sqrt{s^2 + 9}}$$

$$(s^2 + 9)^{(-\frac{1}{2})}$$ = 1/ $$(s^2 + 9)^{(\frac{1}{2})}$$ = $$\frac{1}{\sqrt{s^2 + 9}}$$
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Joined: 30 Jan 2018
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Re: Which of the following expressions is equivalent to (s^2 + 9)^(-1/2) ? [#permalink]

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23 Mar 2018, 02:33
Cant you break (1/root(s^2+9)) further down into (1/root(S +3)) = D?
BSchool Forum Moderator
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GMAT 1: 710 Q49 V36
Re: Which of the following expressions is equivalent to (s^2 + 9)^(-1/2) ? [#permalink]

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23 Mar 2018, 02:47
VincentJongen wrote:
Cant you break (1/root(s^2+9)) further down into (1/root(S +3)) = D?

(s+3)^2 = s^2 + 9 + 6s
since the term 6s is missing we cannot reduce the rt s^2 +9 to s +3
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Re: Which of the following expressions is equivalent to (s^2 + 9)^(-1/2) ? [#permalink]

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26 Mar 2018, 17:37
Bunuel wrote:
Which of the following expressions is equivalent to $$(s^2 + 9)^{(-\frac{1}{2})}$$ ?

A. $$-\frac{s^2 + 9}{2}$$

B. $$-\frac{1}{\sqrt{s^2 + 9}}$$

C. $$-\sqrt{s^2 + 9}$$

D. $$\frac{1}{s+3}$$

E. $$\frac{1}{\sqrt{s^2 + 9}}$$

A negative exponent means that the expression in the numerator must be moved to the denominator. Thus, (s^2 + 9)^-½ is equivalent to 1/(s^2 + 9)^½.

Additionally, an expression raised to the ½ power means that we are to take the square root of that expression. Simplifying the expression, we have:

1/√(s^2 + 9)

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Re: Which of the following expressions is equivalent to (s^2 + 9)^(-1/2) ?   [#permalink] 26 Mar 2018, 17:37
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