SOLUTION: When rewriting an exponential expression with a negative exponent and positive base to an expression containing only a positive exponent, does the sign of the base change? -----

Algebra ->  Exponents -> SOLUTION: When rewriting an exponential expression with a negative exponent and positive base to an expression containing only a positive exponent, does the sign of the base change? -----       Log On


   

Question 448057: When rewriting an exponential expression with a negative exponent and positive base to an expression containing only a positive exponent, does the sign of the base change?
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No; the negative in the exponent means "invert the base";
it does not mean you should change the sign of the base.
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Ex:
y = 10*2^(-t)
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y = 10*(1/2)^t
QUESTION: Please explain what you mean when you say invert the base, it does not mean you should change the sign of the base. Im having a hard time explaning this to my classmates.... I would appreciate help with this....Sincere thanks

Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
When you talk about inversion or inverting, there are 2 basic kinds


1) Additive Inverse: Take any number and change the sign. For example, inverting 2 gives us -2. Inverting -10 gives us 10.


2) Multiplicative Inverse: Take any number and reciprocate it. If this is a whole number, divide by 1 and then flip the fraction. Ex: Invert 2 to get 1%2F2 (note: 2=2%2F1). Ex: Invert 1%2F3 to get 3%2F1=3


So the inverting you're talking about is the multiplicative kind. Why? Because exponents are a condensed way of writing repeated multiplication. For example 3%5E3=3%2A3%2A3 and 3%5E4=3%2A3%2A3%2A3

Divide 3%5E3 by 3%5E4 to get %283%5E3%29%2F%283%5E4%29=%283%2A3%2A3%29%2F%283%2A3%2A3%2A3%29=1%2F3


Also note that %283%5E3%29%2F%283%5E4%29=3%5E%283-4%29=3%5E%28-1%29. So 3%5E%28-1%29=1%2F3


Another way to look at it: When you go from 3%5E3 to 3%5E4, you're multiplying by 3. But to go backwards, you do the opposite of multiplication and you divide by 3, or you multiply by the multiplicative inverse of 3.