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x < 0
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15 Sep 2017, 08:07
15 Sep 2017, 08:07
Expert Reply
00:00
Question Stats:
64% (00:56) correct
35% (00:47) wrong based on 88 sessions
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\(x < 0\)
Quantity A |
Quantity B |
\(((25^x)^{-2})^3)\) |
\(((5^{-3})^2)^{-x}\) |
A) Quantity A is greater.
B) Quantity B is greater.
C) The two quantities are equal.
D) The relationship cannot be determined from the information given.
Re: x < 0
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16 Sep 2017, 08:16
16 Sep 2017, 08:16
1
Using the properties of exponential, we know that if a number is elevated to a and then to b as in (n^a)^b, the exponents can be multiplied and the expression is equal to n^(ab). Thus, in our case we have that column a equals 25^(-6x) and column b equals 5^(6x). Then, given that x<0, this means that 25^(-6x) = 25^(6x), whereas 5^(6x) = 5^(-6x) = 1/5^(6x). Thus, column A is greater and the answer is A.
