Question

How do you simplify `(16xy)/(3x^5y^5)div (8x^2)/(9xy^7)`?

Answer 1

`(16xy)/(3x^5y^5)-:(8x^2)/(9xy^7)=color(blue)((6y^3)/x^5)`

Explanation:

Simplify `(16xy)/(3x^5y^5)-:(8x^2)/(9xy^7)`

When dividing by a fraction, invert the fraction and multiply.

`(16xy)/(3x^5y^5)xx(9xy^7)/(8x^2)`

Simplify and group like terms.

`(144x^1xxx^1xxy^1xxy^7)/(24x^5xxx^2xxy^5)`

Apply product rule `a^m*a^n=a^(m+n)`

`(144x^(1+1)xxy^(1+7))/(24x^(5+2)xxy^5)`

Simplify.

`(6x^2y^8)/(x^7y^5)`

Apply quotient rule `a^m/a^n=a^(m-n)`.

`6x^(2-7)y^(8-5)`

Simplify.

`6x^(-5)y^3`

Apply negative exponent rule `a^(-m)=1/(a^m)`.

`(6y^3)/(x^5)`