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# What is the value of x^(-4)? (1) x^(-2) = 225 (2) x^4 = 1/50,625

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Math Expert
Joined: 02 Sep 2009
Posts: 52390
What is the value of x^(-4)? (1) x^(-2) = 225 (2) x^4 = 1/50,625  [#permalink]

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28 Mar 2018, 22:33
00:00

Difficulty:

5% (low)

Question Stats:

97% (00:44) correct 3% (00:33) wrong based on 40 sessions

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What is the value of $$x^{(-4)}$$?

(1) $$x^{(-2)} = 225$$

(2) $$x^4 = \frac{1}{50,625}$$

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Joined: 07 Dec 2017
Posts: 868
Re: What is the value of x^(-4)? (1) x^(-2) = 225 (2) x^4 = 1/50,625  [#permalink]

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28 Mar 2018, 23:34
Bunuel wrote:
What is the value of $$x^{(-4)}$$?

(1) $$x^{(-2)} = 225$$

(2) $$x^4 = \frac{1}{50,625}$$

As all we're given is equations, we'll look for a simplification-based approach.
This is a Precise methodology.

(1) Since $$(a^b)^c=a^{bc}$$ then we can raise our original expression to the power of 2 to get $$x^{(-4)}= (x^{(-2)})^2 = 225^2$$
Sufficient.

(2) Since $$a^{(-b)} = \frac{1}{a^b}$$ then we know that $$x^{(-4)} = 50,625$$
Sufficient.

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Re: What is the value of x^(-4)? (1) x^(-2) = 225 (2) x^4 = 1/50,625 &nbs [#permalink] 28 Mar 2018, 23:34
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