How do you divide #\frac { 15a ^ { 5} b ^ { 2} } { 5a ^ { 2} b }#?

1 Answer
Jul 4, 2017

See a solution process below:

Explanation:

First, rewrite the expression as:

#(15/5)(a^5/a^2)(b^2/b) => 3(a^5/a^2)(b^2/b)#

Now, use this rule of exponents to divide the #a# term:

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

#3(a^color(red)(5)/a^color(blue)(2))(b^2/b) => 3a^(color(red)(5)-color(blue)(2))(b^2/b) => 3a^3(b^2/b)#

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

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

#3a^3(b^2/b) => 3a^3(b^color(red)(2)/b^color(blue)(1)) => 3a^3b^(color(red)(2)-color(blue)(1)) => 3a^3b^1 =>#

#3a^3b#