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True of false a number raised to a negative power is always a negative number?

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Daniella G. | Recent Graduate in Microbiology, looking to tutor in the sciencesRecent Graduate in Microbiology, looking...
4.7 4.7 (3 lesson ratings) (3)

false. it will only be negative if the number is negative with an odd exponent. what you're actually doing is dividing instead of multiplying. for example:

42 = 16

4-2 = 1/16

basically, it is

x-n =1/xn 


Adrian C. | Patient, Caring, Efficient Math Tutor Specializing in pre- alg to CalcPatient, Caring, Efficient Math Tutor Sp...
5.0 5.0 (65 lesson ratings) (65)

It is false.

Take a look at why negative exponents will never be negative if the number inside is positive.

Suppose we have x2/x3

By law of exponents, we subtract the exponents since the bases are the same.

So x2-3= x-1

And x*x / x*x*x = 1/x

Therefore, x-1 = 1/x

Only time a number to a negative exponent is negative, is when
1) Number inside is negative
2) exponent is an odd number

Nataliya D. | Patient and effective tutor for your most difficult subject.Patient and effective tutor for your mos...

Statement is false. Result can be negative or positive it depends from the base and exponent.

If base is negative number, there are two possibilities: 
  - result is negative, if exponent is odd number; (-2)-3 = 1/(-2)3 = - (1/8)
  - result is positive, if exponent is even number; (-2)-2 = 1/(-2)2 = 1/4

If base is positive number, the result is always positive:
       2-3 = 1/23 = 1/8
       2-2 = 1/22 = 1/4

Very important to remember, if exponent is negative number, that base can't be zero.