Question

(15q^6+5q^2)(5q^4)^-1

Answer 1

(15q^(6)+5q^(2))(5q^(4))^(-1)

1/(5q^(4))*(15q^(6)+5q^(2))

(5q^(2)(3q^(4))+5q^(2)(1))/(5q^(4))

5q^(2)(3q^(4)+1)/5q^(4)

(3q^(4)+1)/q^(2)

Answer 2

Get rid of negative exponent:
(5q^4)^-1 = 1/ 5q^4
(15q^6+5q^2) / 5q^4

Factor out to simplify:
= 5 q^2 ( 3 q^4 + 1) / 5q^4
= ( 3 q^4 + 1)/ q^2