Question

How do you simplify `(\frac { m ^ { 2} n ^ { 3} } { 3n ^ { 4} m ^ { 2} } ) ^ { - 3} * ( \frac { 6p ^ { 3} } { 3p ^ { 3} n } ) ^ { - 2}`?

Answer 1

`(27n^5)/4`

Explanation:

The first step in simplifying is usually to remove the brackets.
But in this case there is quite a lot happening inside each bracket, so let's simplify inside each bracket first.

`((m^2n^3)/(3n^4m^2))^-3 xx ((6p^3)/(3p^3n))^-2`

=`((cancel(m^2))/(3ncancel(m^2)))^-3 xx ((2cancel(p^3))/(cancel(p^3)n))^-2`

A fraction raised to a negative index can be inverted to give a positive index.

=`(3n)^3 xx (n/2)^2`

=`27n^3 xxn^2/4`

=`(27n^5)/4`