Question

How do you evaluate and simplify `16^(3/2)`?

Answer 1

See the entire solution process below:

Explanation:

First, we can use this rule of exponents to rewrite this expression:

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

`16^(3/2) = 16^(color(red)(1/2) xx color(blue)(3)) = (16^color(red)(1/2))^color(blue)(3)`

We can rewrite and simplify this as:

`(16^color(red)(1/2))^color(blue)(3) = (sqrt(16))^color(blue)(3) = 4^color(blue)(3)`

Now, we can simplify this to:
`4^color(blue)(3) = 4 xx 4 xx 4 = 16 xx 4 = 64`