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# Which of the following is equal to 10^-(-3)^2

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Intern
Joined: 10 Jul 2014
Posts: 3
Which of the following is equal to 10^-(-3)^2  [#permalink]

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17 Aug 2014, 02:20
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Difficulty:

5% (low)

Question Stats:

81% (00:31) correct 19% (00:30) wrong based on 186 sessions

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Which of the following is equal to 10^-(-3)^2?

a) 1/10^9

b) 1/10^6

c) 1/10^3

d) 10^6

e) 10^9

I selected D on the understanding that (x^r)^s = x^rs. Eg (x^3)^4 = x^12. So by my working on the above I get:

= 10^-(-6) (because -3 X 2 = -6)
= 10^6

Can someone please explain my error. Thanks!
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Re: Which of the following is equal to 10^-(-3)^2  [#permalink]

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17 Aug 2014, 02:29
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your understanding is correct but application is wrong..

the scenario here is x^(r^s) and not (x^r)^s

in case of x^(r^s) we will raise r to the power of s first and then raise x to the power of (r^s)
so, in this case we will do

10^-(-3)^2 => 10^-(-3^2) => 10^-(9) = 1/(10^9)

Hope it helps!
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Re: Which of the following is equal to 10^-(-3)^2  [#permalink]

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20 Mar 2017, 02:39
-3^2 = 9
therefore 10^ -(-3)^2 = 10^-9 = 1/10^9
Option A
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Re: Which of the following is equal to 10^-(-3)^2  [#permalink]

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26 Aug 2017, 10:48
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JaredL wrote:
Which of the following is equal to 10^-(-3)^2?

a) 1/10^9

b) 1/10^6

c) 1/10^3

d) 10^6

e) 10^9

I selected D on the understanding that (x^r)^s = x^rs. Eg (x^3)^4 = x^12. So by my working on the above I get:

= 10^-(-6) (because -3 X 2 = -6)
= 10^6

Can someone please explain my error. Thanks!

$$10^{-{(-3)}^2}$$

$$10^{-(9)}$$

$$\frac{1}{10^9}$$

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Re: Which of the following is equal to 10^-(-3)^2  [#permalink]

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22 Dec 2018, 19:59
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Re: Which of the following is equal to 10^-(-3)^2   [#permalink] 22 Dec 2018, 19:59
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