How do you multiply #\frac { 12x } { 4} \cdot \frac { x ^ { 9} } { 3x ^ { 5} }#?

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Answer 1 · 2018-01-27T14:15:07

See a solution process below:

First, rewrite the expression as:

#(12/(4 * 3))((x * x^9)/x^5) =>#

#(12/12)((x * x^9)/x^5) =>#

#1((x * x^9)/x^5) =>#

#(x * x^9)/x^5#

Next, use these rules of exponents to multiply the numerator:

#a = a^color(red)(1)# and #x^color(red)(a) xx x^color(blue)(b) = x^(color(red)(a) + color(blue)(b))#

#(x^color(red)(1) * x^color(blue)(9))/x^5 =>#

#x^(color(red)(1)+color(blue)(9))/x^5 =>#

#x^10/x^5#

Now, use this rule of exponents to complete the problem:

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

#x^color(red)(10)/x^color(blue)(5) =>#

#x^(color(red)(10)-color(blue)(5)) =>#

#x^5#