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

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pritis
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If a = -1, what is the value of –(a^2 + a^3 + a^4 + a^5)? [#permalink] New post   08 Jun 2011, 09:35
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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
ShowHide Answer
Official Answer
C
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Re: If a = -1, what is the value of –(a^2 + a^3 + a^4 + a^5)? [#permalink] New post   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] New post   03 Dec 2015, 06:45
on solving

-(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] New post   03 Dec 2015, 07:22
if a = -1, then putting values in equation
= -[ (-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] New post   03 Dec 2015, 07:23
if a = -1, then putting values in equation
= -[ (-1)^2 + (-1)^3 + (-1^4) + (-1^5) ]
= -[ 1 - 1 + 1 - 1 ]
= 0

Answer = C = 0
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Re: If a = -1, what is the value of –(a^2 + a^3 + a^4 + a^5)? [#permalink] New post   03 Dec 2015, 12:24
Bunuel 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


\(- Number^{even}\) = \(+ Number\)

\(- Number^{odd}\) = \(- Number\)

Further there is one more property of the number 1

\(1^{odd/even}\) = \(1\)

From the given numbers we have -

\(a^2+ a^4\) = 1 + 1 =>2

\(a^3 + a^5\) = (-1) + (-1) =>-2

Hence,\(a^2 + a^3 + a^4 + a^5\) = -2 + 2 =>0

Hence answer is (C) 0
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Re: If a = -1, what is the value of –(a^2 + a^3 + a^4 + a^5)? [#permalink] New post   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] New post   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] New post   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] New post   24 Jun 2017, 14:24
\(a = -1\)

\(a^2 + a^3 + a^4 + a^5\)

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

\(1 - 1 + 1 - 1\)

\(0\)

Hence, Answer is C
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Re: If a = -1, what is the value of (a^2 + a^3 + a^4 + a^5)? [#permalink] New post   02 Dec 2023, 07:22
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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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