## redneckboyz 2 years ago Find the quotient. -10d^4e^3f ^5 ÷ 15d 2^e ^2f

1. wio

You 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: $\frac{ -2d^3ef^4 }{ 3}$

2. wio

You can do this even faster if you just subtract exponents on the variables. Realize that $\frac{d^m}{d^n} = d^{m-n}$