How do you multiply #\frac { a ^ { 4} b ^ { 5} } { 3c ^ { 2} } \cdot \frac { 12c ^ { 3} } { 7a ^ { 3} b ^ { 6} }#?

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Answer 1 · 2016-12-21T19:28:10

#(4ac)/(7b)#

First, the rule for multiplying fractions is:

#color(red)(a/b * c/d = (a*c)/(b*d)#

Using this rule we can combine the fractions:

#(a^4b^5 * 12c^3)/(3c^2 * 7a^3b^6)#

#(12a^4b^5c^3)/(21a^3b^6c^2)#

Next we can use two of the rules for exponents to simplify this expression:

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

Using these rules we can simplify as follows:

#(12a^(4-3)c^(3-2))/(21b^(6-5))#

#(12a^1c^1)/(21b^1)#

#(12ac)/(21b)#

Finally, we can simplify the constants:

#((3*4)ac)/((3*7)b)#

#((color(red)(cancel(color(black)(3)))*4)ac)/((color(red)(cancel(color(black)(3)))*7)b)#

#(4ac)/(7b)#