Question

How do you simplify `(9y)(2y^3)^2`?

Answer 1

See the entire simplification process below:

Explanation:

Start the simplification process by using these rule for exponents:

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

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

`(9y)(2^color(red)(1)y^color(red)(3))^color(blue)(2) -> (9y)(2^(color(red)(1)xxcolor(blue)(2))y^(color(red)(3)xxcolor(blue)(2))) -> (9y)(2^2y^6) -> (9y)(4y^6)`

Now, regroup like terms and use these rule of exponents to complete the simplification:

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

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

`(9y)(4y^6) -> (9 xx 4)(y xx y^6) -> 36(y^color(red)(1) xx y^color(blue)(6)) ->`

`36(y^(color(red)(1)+color(blue)(6))) ->`

`36y^7`