Question

How do you multiply `5a ^ { 5} b ^ { 4} \cdot 4c a ^ { 2} b ^ { 2} \cdot 5c a ^ { 5} b ^ { 2}`?

Answer 1

See a solution process below:

Explanation:

First, rewrite this expression as:

`(5 * 4 * 5)(a^5a^2a^5)(b^4b^2b^2)(c * c) =>`

`100(a^5a^2a^5)(b^4b^2b^2)c^2`

Next, use this rule of exponents to simplify the `a` terms:

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

`100(a^color(red)(5)a^color(blue)(2)a^color(green)(5))(b^4b^2b^2)c^2 => 100(a^(color(red)(5) + color(blue)(2) + color(green)(2)))(b^4b^2b^2)c^2 =>`

`100a^12(b^4b^2b^2)c^2`

Use this same rule of exponents to simplify the `b` terms:

`100a^12(b^color(red)(4)b^color(blue)(2)b^color(green)(2))c^2 => 100a^9(b^(color(red)(4)+color(blue)(2)+color(green)(2)))c^2 =>`

`100a^12b^8c^2`