Question

What is the simplified form of `(20x^5)/(15y^6)*(5y^4)/(6x^2)`?

Answer 1

`(10x^3)/(9y^2)`

Explanation:

First, we can rewrite this expression as:

`((20 * 5)(x^5y^4))/((15 * 6)(x^2y^6)) = ((100)(x^5y^4))/((90)(x^2y^6)) = (10(x^5y^4))/(9(x^2y^6))`

Now, we can use these two rules for exponents to simplify the `x` and `y` 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))`

`(10(x^color(red)(5)y^color(red)(4)))/(9(x^color(blue)(2)y^color(blue)(6))) = (10x^(color(red)(5)-color(blue)(2)))/(9y^(color(blue)(6)-color(red)(4))) = (10x^3)/(9y^2)`