Question

How do you simplify `x^-4 (x^2 + x - 3)`?

Answer 1

`= color(blue)(x^-2 + x^-3 - 3.x^-4`

Explanation:

`x^-4 (x^2 + x - 3)`

Here , we need to multiply `color(red)(x^-4` with every term within the bracket.

`color(red)(x^-4) .x^2 +color(red)( x^-4).x^1 -color(red)( x^-4).3`

Note:
`color(blue)(a^m . a^n = a^(m+n)`
Applying the above mentioned property to the exponents of `x`

`= x^(-4+2) + x^(-4+1) - (x^-4).3`
`= x^-2 + x^-3 - (x^-4).3`
`= color(blue)(x^-2 + x^-3 - 3.(x^-4)`