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

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Bunuel
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Which of the following expressions is equivalent to (s^2 + 9)^(-1/2) ? [#permalink] New post   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. \(\frac{1}{\sqrt{s^2 + 9}}\)
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DavidTutorexamPAL
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Which of the following expressions is equivalent to (s^2 + 9)^(-1/2) ? [#permalink] New post   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, \((s^2 + 9)^{(-\frac{1}{2})} = \frac{1}{(s^2 + 9)^{\frac{1}{2}}}\) = \(\frac{1}{\sqrt{s^2 + 9}}\)

(E) is our answer.
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Re: Which of the following expressions is equivalent to (s^2 + 9)^(-1/2) ? [#permalink] New post   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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Re: Which of the following expressions is equivalent to (s^2 + 9)^(-1/2) ? [#permalink] New post   23 Mar 2018, 02:33
Cant you break (1/root(s^2+9)) further down into (1/root(S +3)) = D?
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Re: Which of the following expressions is equivalent to (s^2 + 9)^(-1/2) ? [#permalink] New post   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] New post   26 Mar 2018, 17:37
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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. \(\frac{1}{\sqrt{s^2 + 9}}\)


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)

Answer: E
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Re: Which of the following expressions is equivalent to (s^2 + 9)^(-1/2) ? [#permalink] New post   01 Nov 2021, 00:50
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