Question

How do you simplify `(8x^4y^-3)(1/2x^-5y^2)` and write it using only positive exponents?

Answer 1

See the entire simplification process below:

Explanation:

First, rewrite this expression as:

`(8 xx 1/2)(x^4x^-5)(y^-3y^2)`

`4(x^4x^-5)(y^-3y^2)`

Next, use this rule of exponents to combine the `x` and `y` terms: `x^color(red)(a) xx x^color(blue)(b) = x^(color(red)(a) + color(blue)(b))`

`4(x^color(red)(4) xx x^color(blue)(-5))(y^color(red)(-3) xx y^color(blue)(2)) = 4x^(color(red)(4) + color(blue)(-5))y^(color(red)(-3) + color(blue)(2)) = 4x^-1y^-1`

Now, use these rules for exponents to complete the simplification: `x^color(red)(a) = 1/x^color(red)(-a)` and `a^color(red)(1) = a`

`4x^color(red)(-1)y^color(red)(-1) = 4/(x^color(red)(- -1)y^color(red)(- -1)) = 4/(x^color(red)(1)y^color(red)(1)) = 4/(xy)`