How do you simplify #\frac { 2c ^ { 3} d ^ { - 3} } { 6a ^ { 9} d }#?

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Answer 1 · 2018-01-30T13:35:16

See a solution process below:

First, rewrite the expression as:

#(2/6)(1/a^9)(c^3)(d^-3/d) =>#

#(color(red)(cancel(color(black)(2)))/(color(red)(cancel(color(black)(6)))3))(1/a^9)(c^3)(d^-3/d) =>#

#(1/3)(1/a^9)(c^3)(d^-3/d) =>#

#(c^3/(3a^9))(d^-3/d)#

Next, use these rules of exponents to complete the simplification:

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

#(c^3/(3a^9))(d^color(red)(-3)/d^color(blue)(1)) =>#

#(c^3/(3a^9))(1/d^(color(blue)(1)-color(red)(-3))) =>#

#(c^3/(3a^9))(1/d^(color(blue)(1)+color(red)(3))) =>#

#(c^3/(3a^9))(1/d^4) =>#

#c^3/(3a^9d^4)#