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# If a = -1 and b = –5, then what is the value of a^b(a + 2)^(b + 1)(a +

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Math Expert
Joined: 02 Sep 2009
Posts: 42249

Kudos [?]: 132643 [0], given: 12326

If a = -1 and b = –5, then what is the value of a^b(a + 2)^(b + 1)(a + [#permalink]

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19 Sep 2017, 01:10
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Difficulty:

35% (medium)

Question Stats:

78% (01:13) correct 22% (01:20) wrong based on 83 sessions

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If a = -1 and b = –5, then what is the value of $$a^b(a + 2)^{(b + 1)}(a + 3)^{(b + 2)}(a + 4)^{(b + 3)}(a + 5)^{(b + 4)} =$$

A. 288
B. 1/288
C. -1/288
D. -1/72
E. 0
[Reveal] Spoiler: OA

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Kudos [?]: 132643 [0], given: 12326

Intern
Joined: 31 Jul 2017
Posts: 7

Kudos [?]: 1 [0], given: 0

Re: If a = -1 and b = –5, then what is the value of a^b(a + 2)^(b + 1)(a + [#permalink]

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19 Sep 2017, 02:35
Bunuel wrote:
If a = -1 and b = –5, then what is the value of $$a^b(a + 2)^{(b + 1)}(a + 3)^{(b + 2)}(a + 4)^{(b + 3)}(a + 5)^{(b + 4)} =$$

A. 288
B. 1/288
C. -1/288
D. -1/72
E. 0

-1^-5(1^-4 + 2^-3 + 3^-2 + 4^-1) = -1/288

Kudos [?]: 1 [0], given: 0

Intern
Joined: 16 Jul 2016
Posts: 12

Kudos [?]: 2 [0], given: 28

If a = -1 and b = –5, then what is the value of a^b(a + 2)^(b + 1)(a + [#permalink]

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19 Sep 2017, 03:44
(-1)(1)(1/8)(1/9)(1/4)
-1/288
Ans.C

Kudos [?]: 2 [0], given: 28

Manager
Joined: 17 Aug 2016
Posts: 51

Kudos [?]: 9 [0], given: 26

Re: If a = -1 and b = –5, then what is the value of a^b(a + 2)^(b + 1)(a + [#permalink]

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19 Sep 2017, 13:00
Bunuel wrote:
If a = -1 and b = –5, then what is the value of $$a^b(a + 2)^{(b + 1)}(a + 3)^{(b + 2)}(a + 4)^{(b + 3)}(a + 5)^{(b + 4)} =$$

A. 288
B. 1/288
C. -1/288
D. -1/72
E. 0

$$a^b(a + 2)^{(b + 1)}(a + 3)^{(b + 2)}(a + 4)^{(b + 3)}(a + 5)^{(b + 4)} =$$

=$$(-1)^{(-5)}(-1 + 2)^{(-5 + 1)}(-1 + 3)^{(-5 + 2)}(-1 + 4)^{(-5 + 3)}(-1 + 5)^{(-5 + 4)} =$$

=$$-1*1*\frac{1}{2^3}*\frac{1}{3^2}*\frac{1}{4}$$

=$$\frac{-1}{288}$$

Option C
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Kudos [?]: 9 [0], given: 26

Intern
Joined: 08 Mar 2017
Posts: 27

Kudos [?]: 8 [0], given: 8

Location: India
Concentration: Operations, General Management
GPA: 2.79
WE: Project Management (Manufacturing)
Re: If a = -1 and b = –5, then what is the value of a^b(a + 2)^(b + 1)(a + [#permalink]

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20 Sep 2017, 11:22
Bunuel wrote:
If a = -1 and b = –5, then what is the value of $$a^b(a + 2)^{(b + 1)}(a + 3)^{(b + 2)}(a + 4)^{(b + 3)}(a + 5)^{(b + 4)} =$$

A. 288
B. 1/288
C. -1/288
D. -1/72
E. 0

Since (-1)^-5 makes whole expression negative.

Answer is between C and D

final expression after simplifying -1x 1 x 1/8 x 1/9 x 1/4 =-1/288

Kudos [?]: 8 [0], given: 8

Re: If a = -1 and b = –5, then what is the value of a^b(a + 2)^(b + 1)(a +   [#permalink] 20 Sep 2017, 11:22
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