Question

How do you simplify `(-8/21 x^2y^3) times (-7/16xy^2)`?

Answer 1

See a solution process below:

Explanation:

First, rewrite the expression as:

`(-8/21 xx -7/16)(x^2 xx x)(y^3 xx y^2) =>`

`(-color(red)(cancel(color(black)(8)))/(color(blue)(cancel(color(black)(21))3)) xx -color(blue)(cancel(color(black)(7)))/(color(red)(cancel(color(black)(16)))2))(x^2 xx x)(y^3 xx y^2) =>`

`(-1/3 xx -1/2)(x^2 xx x)(y^3 xx y^2) =>`

`1/6(x^2 xx x)(y^3 xx y^2)`

Next, use this rule for exponents to rewrite the `x` term:

`a = a^color(red)(1)`

`1/6(x^2 xx x)(y^3 xx y^2) => 1/6(x^2 xx x^color(red)(1))(y^3 xx y^2)`

Now, use this rule of exponents to simplify the `x` and `y` terms:

`x^color(red)(a) * x^color(blue)(b) = x^(color(red)(a)+color(blue)(b))`

`1/6(x^color(red)(2) xx x^color(blue)(1))(y^color(red)(3) xx y^color(blue)(2)) =>`

`1/6x^(color(red)(2)+color(blue)(1))y^(color(red)(3)+color(blue)(2)) =>`

`1/6x^3y^5`

Or

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