Question

How do you evaluate `\frac { ( 8\sqrt { 12} ) ^ { 2} } { 24}`?

Answer 1

See the entire solution process below:

Explanation:

First, use this rule for exponents and this rule for radicals to rewrite this expression:

`root(color(red)(n))(x) = x^(1/color(red)(n))` and `a = a^color(red)(1)`

`((8sqrt(12))^2)/24 = (8(root(2)(12))^2)/24 = (8^color(red)(1)12^(1/color(red)(2)))^2/24`

Next, use this rule of exponents to further evaluate the numerator:

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

`((8^color(red)(1)12^color(red)(1/2))^color(blue)(2))/24 = (8^(color(red)(1) xx color(blue)(2))12^(color(red)(1/2) xx color(blue)(2)))/24 = (8^2 * 12^1)/24 = (64 * 12)/24 = 768/24 =`

`32`