Question

How do you simplify `100^(-3/2)`?

Answer 1

See full explanation below:

Explanation:

First, we need to understand the following exponent rule:

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

The reverse is also true:

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

We can modify this expression as follows using these rules:

`100^(-3/2) = 100^(color(red)(1/2) xx color(blue)(-3)) = (100^(1/2))^-3`

We can now simplify the term within parenthesis:

`(100^(1/2))^-3 = 10^-3`

Next we need to understand this rule for exponents:

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

Applying this rule to our problem gives:

`10^color(red)(-3) = 1/10^color(red)(- -3) = 1/10^color(red)(3) = 1/(10 xx 10 xx 10) = 1/1000` or `0.001`