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wio
 2 years ago
Best ResponseYou've already chosen the best response.2You wanna factor things out a bit: \[ 10d^4e^3f^5 = (1)(2)(5)(d)(d)(d)(d)(e)(e)(e)(f)(f)(f)(f)(f) \\ 15de^2f = (3)(5)(d)(e)(e)(f) \]So our fraction is now: \[ \frac{(1)(2)(5)(d)(d)(d)(d)(e)(e)(e)(f)(f)(f)(f)(f)} {(3)(5)(d)(e)(e)(f)} \] Then you wanna cancel things out. Both have 5, cancel them: \[ \frac{ (1)(2)(d)(d)(d)(d)(e)(e)(e)(f)(f)(f)(f)(f) }{ (3)(d)(e)(e)(f) } \] Both have d: \[ \frac{ (1)(2)(d)(d)(d)(e)(e)(e)(f)(f)(f)(f)(f) }{ (3)(e)(e)(f) } \] Both have 2 'e's: \[ \frac{ (1)(2)(d)(d)(d)(e)(f)(f)(f)(f)(f) }{ (3)(f) } \] Both have f: \[ \frac{ (1)(2)(d)(d)(d)(e)(f)(f)(f)(f) }{ (3) } \] We simplify: \[ \frac{ 2d^3ef^4 }{ 3} \]

wio
 2 years ago
Best ResponseYou've already chosen the best response.2You can do this even faster if you just subtract exponents on the variables. Realize that \[ \frac{d^m}{d^n} = d^{mn} \]
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