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# If a = -1, what is the value of –(a^2 + a^3 + a^4 + a^5)?

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Intern
Joined: 03 Jun 2011
Posts: 8

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If a = -1, what is the value of –(a^2 + a^3 + a^4 + a^5)? [#permalink]

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08 Jun 2011, 09:35
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Difficulty:

5% (low)

Question Stats:

91% (00:22) correct 9% (00:14) wrong based on 47 sessions

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If a = -1, what is the value of –(a^2 + a^3 + a^4 + a^5)?

A -14
B -4
C 0
D 4
E 14
[Reveal] Spoiler: OA

Kudos [?]: 3 [0], given: 2

Math Forum Moderator
Joined: 20 Dec 2010
Posts: 1965

Kudos [?]: 2100 [0], given: 376

Re: If a = -1, what is the value of –(a^2 + a^3 + a^4 + a^5)? [#permalink]

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08 Jun 2011, 09:46
pritis wrote:
If a = -1, what is the value of –(a^2 + a^3 + a^4 + a^5)?
Choices
A -14
B -4
C 0
D 4
E 14

Even power of negative=+ve
Odd power of negative=-ve

$$a^2=(-1)^2=1$$
$$a^3=(-1)^3=-1$$
$$a^4=(-1)^4=1$$
$$a^5=(-1)^5=-1$$

Ans: "C"

pritis:
Please use ^ to denote power.
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Kudos [?]: 2100 [0], given: 376

Director
Joined: 04 Dec 2015
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Location: India
Concentration: Technology, Strategy
Schools: ISB '19, IIMA , IIMB, XLRI
WE: Information Technology (Consulting)
Re: If a = -1, what is the value of –(a^2 + a^3 + a^4 + a^5)? [#permalink]

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21 Jun 2017, 22:53
pritis wrote:
If a = -1, what is the value of –(a^2 + a^3 + a^4 + a^5)?

A. -14
B. -4
C. 0
D. 4
E. 14

$$–(a^2 + a^3 + a^4 + a^5)$$

$$–((-1)^2 + (-1)^3 + (-1)^4 + (-1)^5)$$

$$–(1-1 +1 -1) = -(0) = 0 .$$ Answer C...

Kudos [?]: 320 [0], given: 261

Senior Manager
Joined: 28 Jun 2015
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Kudos [?]: 109 [0], given: 47

Concentration: Finance
GPA: 3.5
Re: If a = -1, what is the value of –(a^2 + a^3 + a^4 + a^5)? [#permalink]

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21 Jun 2017, 23:16
$$a = -1$$
$$a^2 = 1$$
$$a^3 = -1$$
$$a^4 = 1$$
$$a^5 = -1$$

$$-(a^2 + a^3 + a^4 + a^5) = -(1 - 1 + 1 - 1) = 0.$$
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Kudos [?]: 109 [0], given: 47

BSchool Forum Moderator
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Re: If a = -1, what is the value of –(a^2 + a^3 + a^4 + a^5)? [#permalink]

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21 Jun 2017, 23:30
If the number(x) is negative, x^even = positive and x^odd = negative

The expression(which contains 2 even powers and 2 odd powers of x), cancel each other out.
Since the number is 1, they have the same magnitude.
The sum will be 0(Option C)
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Kudos [?]: 696 [0], given: 17

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Joined: 19 Mar 2014
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Re: If a = -1, what is the value of –(a^2 + a^3 + a^4 + a^5)? [#permalink]

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24 Jun 2017, 14:24
$$a = -1$$

$$a^2 + a^3 + a^4 + a^5$$

$$(-1)^2 + (-1)^3 + (-1)^4 + (-1)^5$$

$$1 - 1 + 1 - 1$$

$$0$$

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Re: If a = -1, what is the value of –(a^2 + a^3 + a^4 + a^5)?   [#permalink] 24 Jun 2017, 14:24
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