Question

How do you multiply `(3a ^ { 2} b ^ { 3} ) ( 7a b ^ { 3} )`?

Answer 1

See the entire solution process below:

Explanation:

First, rewrite this expression as:

`(3 * 7)(a^2a)(b^3b^3) = 21(a^2a)(b^3b^3)`

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

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

`21(a^2a)(b^3b^3) = 21(a^color(red)(2)a^color(blue)(1))(b^color(red)(3)b^color(blue)(3)) = 21a^(color(red)(2) + color(blue)(1))b^(color(red)(3) + color(blue)(3)) =`

`21a^3b^6`