How do you simplify the expression #(12a^-3b^9)/(21a^2b^-5)# using the properties?

1 Answer
Apr 23, 2017

Answer:

See the entire solution process below:

Explanation:

First, rewrite this expression as:

#(12/21)(a^-3/a^2)(b^9/b^-5) => ((3 xx 4)/(3 xx 7))(a^-3/a^2)(b^9/b^-5) =>#

#((color(red)(cancel(color(black)(3))) xx 4)/(color(red)(cancel(color(black)(3))) xx 7))(a^-3/a^2)(b^9/b^-5) => 4/7(a^-3/a^2)(b^9/b^-5)#

Now, use these two rules of exponents to simplify the #a# and #b# terms:

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

#4/7(a^color(red)(-3)/a^color(blue)(2))(b^color(red)(9)/b^color(blue)(-5)) => 4/7(1/a^(color(blue)(2)-color(red)(-3)))(b^(color(red)(9)-color(blue)(-5))) =>#

#4/7(1/a^(color(blue)(2)+color(red)(3)))(b^(color(red)(9)+color(blue)(5))) => 4/7(1/a^5)(b^14) => (4 * 1 * b^14)/(7 * a^5) =>#

#(4b^14)/(7a^5)#