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# x < 0

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x < 0 [#permalink]  15 Sep 2017, 08:07
Expert's post
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Question Stats:

48% (00:31) correct 51% (00:35) wrong based on 27 sessions

$$x < 0$$

 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.
[Reveal] Spoiler: OA

_________________
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Re: x < 0 [#permalink]  16 Sep 2017, 08:16
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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.
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Re: x < 0 [#permalink]  13 Nov 2018, 17:04
can any one elaborate this with example?
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Re: x < 0 [#permalink]  19 Nov 2018, 16:47
AE wrote:
can any one elaborate this with example?

Hi

It is basically the powers multiplied.

For example if it were (2^2)^3 then it would be 2^6 the rules of exponentials.

Similarly we know that quantity A will have a negative exponent while Quantity B will have a positive exponent

Since x < 0 that means x will be negative. As a result, quantity A will have a positive exponent and quantity B will have a negative exponent.

25^(-6x) << quantity A

25^(6x) << quantity B

I hope this helps.
Re: x < 0   [#permalink] 19 Nov 2018, 16:47
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