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If x = -1, then x^(-3) + x^(-2) + x^2 + x^3 =

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Bunuel
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If x = -1, then x^(-3) + x^(-2) + x^2 + x^3 = [#permalink] New post   17 Oct 2020, 13:11
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A
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C
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If \(x = -1\), then \(x^{-3} + x^{-2} + x^2 + x^3 =\)

(A) -2
(B) -1
(C) 0
(D) 1
(E) 2
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C
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Re: If x = -1, then x^(-3) + x^(-2) + x^2 + x^3 = [#permalink] New post   17 Oct 2020, 20:07
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Bunuel wrote:
If \(x = -1\), then \(x^{-3} + x^{-2} + x^2 + x^3 =\)

(A) -2
(B) -1
(C) 0
(D) 1
(E) 2


By the law of exponents, \(a^{-m} = \frac{1}{a^m}\)


The expression can therefore be re written as \(\frac{1}{x^3} + \frac{1}{x^2} + x^2 + x^3\)


Putting x = -1, we get \(\frac{1}{(-1)^3} + \frac{1}{(-1)^2} + (-1)^2 + (-1)^3 = \frac{1}{-1} + \frac{1}{1} + 1 - 1\)


= -1 + 1 + 1 - 1 = 0



Option C

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Re: If x = -1, then x^(-3) + x^(-2) + x^2 + x^3 = [#permalink] New post   17 Oct 2020, 21:57
x^(-3)+x^(-2)+x^2+x^3=-1+1+1-1=0 C)
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Re: If x = -1, then x^(-3) + x^(-2) + x^2 + x^3 = [#permalink] New post   18 Oct 2020, 00:40
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\(x^{-3} + x^{-2} + x^{2} + x^{3}\)

=> \(\frac{1 }{ x^{3}} + \frac{1 }{ x^{2}} + x^{2} + x^{3}\)

For x = -1:

=> \(\frac{1 }{ (-1)^{3}} + \frac{1 }{ (-1)^{2}} + (-1)^{2} + (-1)^{3}\)

=> -1 + 1 + 1 - 1 = 0

Answer C
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Re: If x = -1, then x^(-3) + x^(-2) + x^2 + x^3 = [#permalink] New post   18 Oct 2020, 01:50
Asked: If \(x = -1\), then \(x^{-3} + x^{-2} + x^2 + x^3 =\)

\(x^{-3} + x^{-2} + x^2 + x^3 = -1 + 1 +1 - 1 = 0\)

IMO C
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If x = –1, then x^(–3) + x^(–2) + x^2 + x^3 = [#permalink] New post   11 Dec 2020, 10:31
IMO C

-1 raised to even power would result in a positive 1.
-1 raised to odd power would result in negative 1.

\( x^-2= \frac{1}{x^2} \) or \(x^-3=\frac{1}{x^3}\)

The signs are retained in the reciprocals as well.

Hence answer \(x^-3 + x^-2 + x^2 + x^3\) = -1 +1 +1 -1 =0

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Re: If x = –1, then x^(–3) + x^(–2) + x^2 + x^3 = [#permalink] New post   14 Dec 2020, 08:17
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Bunuel wrote:
If x = –1, then \(x^{–3} + x^{–2} + x^2 + x^3 =\)

(A) –2
(B) –1
(C) 0
(D) 1
(E) 2

Solution:

Since -1 raised to an odd power is -1 and raised to an even power is 1, the expression is equal to -1 + 1 + 1 + (-1) = 0.

(Note that in the case of having -1 as the base, it doesn’t matter if we raise -1 to an odd positive power or to an odd negative power: the outcome will be -1. Similarly, when the base is -1, it doesn’t matter if -1 is raised to an even positive exponent or an even negative exponent: the outcome will be 1.)

Answer: C
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Re: If x = -1, then x^(-3) + x^(-2) + x^2 + x^3 = [#permalink] New post   15 Mar 2023, 12:09
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Re: If x = -1, then x^(-3) + x^(-2) + x^2 + x^3 = [#permalink]
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