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Question
Simplify, giving Solution with positive index
`((5"x"^7)^3 . (10"x"^2)^2)/(2"x"^6)^7 = (5^3 "x"^(7xx3) . 10^2 . "x"^(2xx2))/(2^7. "x"^(6xx7))`
Solution
`((5"x"^7)^3 . (10"x"^2)^2)/(2"x"^6)^7 = (5^3 "x"^(7xx3) . 10^2 . "x"^(2xx2))/(2^7. "x"^(6xx7))`
`= 5^3 . 10^2 . 2^-7 "x"^(21+4-42)`
`= (5^3 xx 10^2)/(2^7 "x"^17) = (5 xx 5 xx 5 xx 2 xx 5 xx 2 xx 5)/(2 xx 2 xx 2 xx 2 xx 2 xx 2 xx 2. "x"^17)`
`= 5^5/(2^5 "x"^17) = 3125/(32"x"^17)`
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