Question

How do you multiply `(4a ^ { 2} ) ^ { 0} ( 2a ^ { 3} ) ^ { 2}`?

Answer 1

See a solution process below:

Explanation:

First, we can use this rule of exponents to simplify the term on the left:

`a^color(red)(0) = 1`

`(4a^2)^color(red)(0)(2a^3)^2 => 1(2a^3)^2 => (2a^3)^2`

Now, we can use these two rules of exponents to complete the multiplication:

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

`(2a^3)^2 => (2^color(red)(1)a^color(red)(3))^color(blue)(2) => 2^(color(red)(1) xx color(blue)(2))a^(color(red)(3) xx color(blue)(2)) => 2^2a^6 => 4a^6`