How do you simplify #(-12c^3d^0f^-2)/(6c^5d^-3f^4)#?

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Answer 1 · 2017-06-18T16:15:15

See a solution process below:

First, rewrite this expression as:

#(-12/6)(c^3/c^5)(d^0/d^-3)(f^-2/f^4) => #

#-2(c^3/c^5)(d^0/d^-3)(f^-2/f^4)#

Next, use this rule of exponents to simplify the #d# term:

#x^color(red)(a)/x^color(blue)(b) = x^(color(red)(a)-color(blue)(b))#

#-2(c^3/c^5)(d^color(red)(0)/d^color(blue)(-3))(f^-2/f^4) =>#

#-2(c^3/c^5)(d^(color(red)(0)-color(blue)(-3)))(f^-2/f^4) =>#

#-2(c^3/c^5)(d^(color(red)(0)+color(blue)(3)))(f^-2/f^4) =>#

#-2(c^3/c^5)d^3(f^-2/f^4)#

Now, use this rule of exponents to simplify the #c# and #f# terms:

#x^color(red)(a)/x^color(blue)(b) = 1/x^(color(blue)(b)-color(red)(a))#

#-2(c^color(red)(3)/c^color(blue)(5))d^3(f^color(red)(-2)/f^color(blue)(4)) =>#

#-2(1/c^(color(blue)(5)-color(red)(3)))d^3(1/f^(color(blue)(4)-color(red)(-2))) =>#

#-2(1/c^2)d^3(1/f^(color(blue)(4)+color(red)(2))) =>#

#-2(1/c^2)d^3(1/f^6) =>#

#(-2d^3)/(c^2f^6)#