How do you simplify #(100x^3y^5)/(36xy^8)#?

1 Answer
May 19, 2017

Answer:

See a solution process below:

Explanation:

First, rewrite the expression as:

#100/36(x^3/x)(y^5/y^8) => (4 xx 25)/(4 xx 9)(x^3/x)(y^5/y^8) =>#

#(color(red)(cancel(color(black)(4))) xx 25)/(color(red)(cancel(color(black)(4))) xx 9)(x^3/x)(y^5/y^8) => 25/9(x^3/x)(y^5/y^8)#

Next, use these two rules of exponents to simplify the #x# terms:

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

#25/9(x^3/x)(y^5/y^8) => 25/9(x^color(red)(3)/x^color(blue)(1))(y^5/y^8) => 25/9x^(color(red)(3)-color(blue)(1))(y^5/y^8) =>#

#(25x^2)/9(y^5/y^8)#

Now, use this rule of exponents to simplify the #y# term:

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

#(25x^2)/9(y^color(red)(5)/y^color(blue)(8)) => (25x^2)/9 * 1/y^(color(blue)(8)-color(red)(5)) => (25x^2)/9 * 1/y^3 =>#

#(25x^2)/(9y^3)#