Question

How do you multiply `(x ^ { 7} ) ^ { 2} \cdot ( x ^ { 4} ) ^ { 5}`?

Answer 1

See the entire solution process below:

Explanation:

First, use this rule of exponents to eliminate the outer exponents:

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

`(x^color(red)(7))^color(blue)(2) * (x^color(red)(4))^color(blue)(5) = x^(color(red)(7) xx color(blue)(2)) * x^(color(red)(4) xx color(blue)(5)) = x^14 * x^20`

Now, use this rule of exponents to complete the problem:

`x^color(red)(14) xx x^color(blue)(20) = x^(color(red)(14) + color(blue)(20)) = x^34`