SOLUTION: Concerning negative exponents, why is the reciprocal of a fraction a positive one in the numerator? Instead of a negative one. e.g. 6^-3 = 1 / 6^3 vs. 6^-3 = -1 / 6^3

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Question 1198534: Concerning negative exponents, why is the reciprocal of a fraction a positive one in the numerator? Instead of a negative one.
e.g.
6^-3 = 1 / 6^3 vs. 6^-3 = -1 / 6^3
Found 3 solutions by MathLover1, MathTherapy, math_tutor2020:
Answer by MathLover1(20849)   (Show Source): You can put this solution on YOUR website!

Negative exponents denote a reciprocal value. A number raised to a negative power is equal to over the number raised to the opposite power.
so,
Answer by MathTherapy(10552)   (Show Source): You can put this solution on YOUR website!

Concerning negative exponents, why is the reciprocal of a fraction a positive one in the numerator? Instead of a negative one.
e.g.
6^-3 = 1 / 6^3 vs. 6^-3 = -1 / 6^3 
6-3 =  vs. 6-3 = 
6-3 =  = .
As seen above, the 6 in the numerator and the 1 in the denominator are BOTH positive. They can't,
all of a sudden, become negative. Then, they TRADE PLACES, but DEFINITELY remain positive.
They can't, all of a sudden, become negative.

Now, if we had: (- 6)-3, then that's the same as: , which would then be:.

                          then becomes: , which can also be written as: 

As seen above, either the numerator, 1, or the denominator, 6, can be negative, as a result of the - 6 that was given!
Answer by math_tutor2020(3817)   (Show Source): You can put this solution on YOUR website!

Recall that
We add the exponents b and c. The base must stay the same the entire time.

Example:


Also, recall that raising any nonzero value to the zeroth power gets us 1.
where x is nonzero
Example


What we can do is the following steps




use the a^b*a^c = a^(b+c) rule mentioned earlier.

Then replace the 6^0 with 1 and isolate the term




------------------------------------------------

In general:







where

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