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