Negative Exponents

Negative exponents have nothing to do with negative numbers.

If we think of the use of negative exponents in Scientific Notation we can understand them a bit better.



A negative exponent with a power of 10 means it is a decimal.




10 to the -3 = 0.001, which we can also write as 1 over 1000.





When we use powers of 10 in Scientific Notation we are changing the negative power to a decimal and multiplying it by the significant digits.




Significant digits = 2.63

10 to -3 = 0.001

Multiply and you have 0.00263









A negative exponent means "the reciprocal"


2 to the -3 can be rewritten as 1 over 2 to the 3rd (or 2 cubed).

2 cubed is 8.

Our final answer is one over eight.





When we are simplifying a more complex problem that includes a negative exponent we:





reduce any fractions

combine the exponets for each base:

x
and
y

Finally put any negative exponents in the opposite area of the fraction:


If there is a negative in the numerartor -> put it in the denominator.

If there is a negative in the denominator -> put it in the numerator.

Your final answer should never include a negative exponent.