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

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Answer 1 · 2017-05-19T13:57:32

See a solution process below:

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:

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

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

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

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