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A and C are negative, so they can't be right, because the other answers are positive. in B and E, we're raising an integer greater than 1 to a negative power, so we'll end up with a value between 0 and 1. Only answer D is greater than 1, so it is largest.
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Asked: Which of the following has the greatest value?

(A) −5^6
Negative
(B) 6^−5
Less than 1
(C) (−6)^5
Negative
(D) (−5)^6
5^6; very large positive
(E) 5^−6
Less than 1

IMO D

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Sajjad1994
Which of the following has the greatest value?

(A) −5^6

(B) 6^−5

(C) (−6)^5

(D) (−5)^6

(E) 5^−6
Solution:

We can eliminate choice A because the result is a negative value. We can eliminate choices B and E because each is a positive number greater than 1 that is raised to a negative power, resulting in a fraction that is between 0 and 1.Choice C is a negative number raised to an odd power, and this yields a negative number. Finally, we see that choice D is a negative number raised to an even power, and this yields a positive number greater than 1; thus, (−5)^6 is the greatest of the 5 choices.

Answer: D
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