How do you solve this (-2)^-3?

Question

How do you solve this (-2)^-3?

Answer 1

-2ֿ³ = 0.125

Answer 2

So couple of rules: any neg exponent is the reciprocal (basically the number you times it by to get one so put it under one)

ie:

the recipocal of 2 is 1/2      

           2 x 1/2 = 1



the recipocal of 3 is 1/3        

           3 x 1/3 = 1

neg numbers alternate positive to neg when they are multiplied out ie:

-2 x -2 = 4     and -2 x -2 x -2 = -8

so       (factoring out)       -2 x -2 x -2 = -8    

Then give it a reciprocal     (-1/8)

This is your answer it is quite simple when you learn the rules

(-1/8)

Answer 3

A number raised to a negative integer exponent is defined as one over the number raised to the positive integer exponent.In other words,

x^(-a) = 1/(x^a)

In this case, x = -2 and a = 3.

(-2)^(-3) = 1 / ((-2)^3) = 1 / (-2 * -2 * -2) = 1 / (-8)

So, the answer is -1/8

Answer 4

The rules to know for this problem are:

1) a nonzero number to the −1 power produces its reciprocal.

2) a^n = a x a x a x a .... n times

Use rule 1 to evaluate a^-n

a^-n = (a^n)^-1 = 1/a^n

(-2)¯³ = 1/(-2)³

Now use rule 2 to evaluate (a)^n

1/(-2)³ = (1/-2) x (1/-2) x (1/-2) = (1/4) x (1/-2) = 1/-8 = -1/8