Question

How to evaluate a number with a negative fraction exponent?

Answer 1

To evaluate a number with a negative fraction exponent, you need to take care of two things.
1) The negative exponent.
2) The fraction as an exponent.

1) Negative exponent


`a^(-n) = (1)/(a^n)`

2) Fractional exponent


`a^{(m)/(n)} = \sqrt[n] {a^m} = (\sqrt[n]{a})^m`

Example:

Evaluate


`8^{- (2)/(3)}`

First, take care of the negative exponent.


`8^{-(2)/(3)} = \frac{1}{8^{(2)/(3)}}=`

Now we take care of the fractional exponent by using a root.


`= \frac{1}{\sqrt[3] {8^2}} = \frac{1}{(\sqrt[3] {8})^2} =`


`= (1)/(2^2) = (1)/(4)`