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

Question

Abigail Allen · Accepted Answer

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)#

Jace Anderson · Answer

undefined To simplify the expression (-12c^3d^0f^-2)/(6c^5d^-3f^4), you need to simplify each term separately and then divide them.

(-12/6) = -2
(c^3/c^5) = c^(-5-3) = c^(-8)
(d^0/d^-3) = d^(0-(-3)) = d^3
(f^-2/f^4) = f^(-2-4) = f^(-6)

So, the simplified expression is: -2c^-8d^3f^-6