How do you simplify (9y)(2y^3)^2(9y)(2y3)2?

1 Answer
Feb 1, 2017

See the entire simplification process below:

Explanation:

Start the simplification process by using these rule for exponents:

a = a^color(red)(1)a=a1

(x^color(red)(a))^color(blue)(b) = x^(color(red)(a) xx color(blue)(b))(xa)b=xa×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)(9y)(21y3)2(9y)(21×2y3×2)(9y)(22y6)(9y)(4y6)

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

a = a^color(red)(1)a=a1

x^color(red)(a) xx x^color(blue)(b) = x^(color(red)(a) +color(blue)(b))xa×xb=xa+b

(9y)(4y^6) -> (9 xx 4)(y xx y^6) -> 36(y^color(red)(1) xx y^color(blue)(6)) ->(9y)(4y6)(9×4)(y×y6)36(y1×y6)

36(y^(color(red)(1)+color(blue)(6))) ->36(y1+6)

36y^736y7