Question

How do you simplify `(7x^-4 y^5) (2x^-3 y^-4)`?

Answer 1

See the entire simplification process below:

Explanation:

First, rewrite the expression as:

`(7 xx 2)(x^-4 * x^-3)(y^5 * y^-4) = 14(x^-4 * x^-3)(y^5 * y^-4)`

Next, use this rule of exponents to multiply the variables:

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

`14(x^color(red)(-4) * x^color(blue)(-3))(y^color(red)(5) * y^color(blue)(-4)) = 14x^(color(red)(-4) + color(blue)(-3))y^(color(red)(5) + color(blue)(-4)) = 14x^-7y^1`

Then, use this rule of exponents to complete the simplification for the `y` variable:

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

`14x^-7y^color(red)(1) = 14x^-7y`

Now, use this rule of exponents to complete the simplification:

`x^color(red)(a) = 1/x^color(red)(-a)`

`14x^color(red)(-7)y = (14y)/x^color(red)(- -7) = (14y)/x^7`