Question

How do you evaluate `(\frac { 3} { 2} ) ^ { - 5}`?

Answer 1

See the entire solution process below:

Explanation:

First, we can use these to rules for exponents to begin the evaluation process:

`a = a^color(red)(1)` and `(x^color(red)(a))^color(blue)(b) = x^(color(red)(a) xx color(blue)(b))`

`(3/2)^5 = (3^color(red)(1)/2^color(red)(1))^color(blue)(-5) = 3^(color(red)(1)xxcolor(blue)(-5))/2^(color(red)(1)xxcolor(blue)(-5)) = 3^-5/2^-5`

Next, we use these rules of exponents to complete the evaluation of the expression:

`x^color(red)(a) = 1/x^color(red)(-a)` and `1/x^color(blue)(a) = x^color(blue)(-a)`

`3^color(red)(-5)/2^color(blue)(-5) = 2^color(blue)(- -5)/3^color(red)(- -5) = 2^color(blue)(5)/3^color(red)(5) = 32/243`