Search
Ask a question
0

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

Give an example to support your answer 

3 Answers by Expert Tutors

Tutors, sign in to answer this question.
Daniella G. | Recent Graduate in Microbiology, looking to tutor in the sciencesRecent Graduate in Microbiology, looking...
4.7 4.7 (3 lesson ratings) (3)
1

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 (22 lesson ratings) (22)
0

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...
0

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.