Question

Simplify, giving Solution with positive index

`((7 "p"^2 "q"^9 "r"^5)^2 (4 "pqr")^3)/(14 "p"^6 "q"^10 "r"^4)^2`

Answer 1

`((7 "p"^2 "q"^9 "r"^5)^2 (4 "pqr")^3)/(14 "p"^6 "q"^10 "r"^4)^2`

`= (7^2 "p"^(2xx2) "q"^(9xx2) "r"^(5xx2) (4^3 "p"^3 "q"^3 "r"^3))/(14^2 "p"^(6xx2) "q"^(10xx2) "r"^(4xx2))`

`= (7 xx 7 "p"^4 "q"^18 "r"^10 . 4 xx 4 xx 4  "p"^3 "q"^3 "r"^3)/(2 xx 7 xx 2 xx 7 xx  "p"^12  "q"^20  "r"^8)`

`= "p"^(4 - 12 + 3) "q"^(18-20+3) "r"^(10 - 8 + 3) 4 xx 4`

`= 16"p"^(-5) "qr"^5`

`= (16"qr"^5)/"p"^5`