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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
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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88% (01:23) correct 12% (00:14) wrong based on 34 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
Math Forum Moderator
Joined: 20 Dec 2010
Posts: 2010
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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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...
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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, 23:16
$$a = -1$$
$$a^2 = 1$$
$$a^3 = -1$$
$$a^4 = 1$$
$$a^5 = -1$$

$$-(a^2 + a^3 + a^4 + a^5) = -(1 - 1 + 1 - 1) = 0.$$
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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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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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