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redneckboyz
Find the quotient. -10d^4e^3f ^5 ÷ 15d 2^e ^2f
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: \[ \frac{ -2d^3ef^4 }{ 3} \]
You can do this even faster if you just subtract exponents on the variables. Realize that \[ \frac{d^m}{d^n} = d^{m-n} \]