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

Daniella G. | Recent Graduate in Microbiology, looking to tutor in the sciencesRecent Graduate in Microbiology, looking...
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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

what does 4^-2 mean

Adrian C. | Patient, Caring, Efficient Math Tutor Specializing in pre- alg to CalcPatient, Caring, Efficient Math Tutor Sp...
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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...
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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.