How do you multiply and simplify #\frac { a ^ { 3} b ^ { 4} } { 14c } \cdot \frac { 4a c } { b }#?

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Answer 1 · 2017-07-20T01:05:13

See a solution process below:

First, rewrite the expression as:

#4/14(a^3 * a)(b^4/b)(c/c) =>#

#4/14(a^3 * a)(b^4/b) * 1 =>#

#4/14(a^3 * a)(b^4/b) =>#

#(2 xx 2)/(2 xx 7)(a^3 * a)(b^4/b) =>#

#(color(red)(cancel(color(black)(2))) xx 2)/(color(red)(cancel(color(black)(2))) xx 7)(a^3 * a)(b^4/b) =>#

#2/7(a^3 * a)(b^4/b)#

Next, use these rules of exponents to multiply the #a# terms:

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

#2/7(a^3 * a)(b^4/b) =>#

#2/7(a^color(red)(3) * a^color(blue)(1))(b^4/b) =>#

#2/7(a^(color(red)(3)+color(blue)(1)))(b^4/b) =>#

#2/7(a^4)(b^4/b) =>#

#(2a^4)/7(b^4/b)#

Now, use these rules of exponents to evaluate the #b# terms:

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

#(2a^4)/7(b^4/b) =>#

#(2a^4)/7(b^color(red)(4)/b^color(blue)(1)) =>#

#(2a^4)/7(b^(color(red)(4)-color(blue)(1))) =>#

#(2a^4)/7(b^3) =>#

#(2a^4b^3)/7#