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

1 Answer
smendyka
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)

(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

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