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

Question

If  x = -1 , then  x^{-3} + x^{-2} + x^2 + x^3 =

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

CrackverbalGMAT · Answer

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

Arun Kumar

gmatcafe · Answer

x^(-3)+x^(-2)+x^2+x^3=-1+1+1-1=0 C)

MathRevolution · Answer

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

Kinshook · Answer

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

kriswati · Answer

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

Posted from my mobile device

ScottTargetTestPrep · Answer

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

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

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