Question

How do you multiply `np ^ { 0} \cdot 4p m ^ { - 4} n ^ { 3} \cdot 2m ^ { 0} n ^ { - 3}p`?

Answer 1

`(8np^2)/m^4`

Explanation:

When you are working with indices there a number of laws which you can use. Decide what you want to do first. NO law is more important than another.

I prefer to sort out the negative and 0 indices first.

Recall: `color(red)(x^-m = 1/x^m) " and " color(blue)(x^0 = 1) (x !=0)`

`n color(blue)(p^0) xx 4p color(red)(m^-4)n^3 xx2 color(blue)(m^0)color(red)(n^-3)p`

=`n color(blue)((1)) xx (4pn^3)/ color(red)(m^4) xx(2 color(blue)((1))p)/color(red)(n^3)`

Now simplify the numerators and denominators separately.

=`(8n^4p^2)/(m^4n^3)`

Subtract the indices of like bases.

=`(8np^2)/m^4`