Question

How do you get rid of the negative exponents and simplify `(\frac { 12m ^ { 2} n ^ { 3} p ^ { - 9} } { 20m ^ { - 7} n ^ { - 3} p ^ { - 6} } ) ^ { - 1}`?

Answer 1

`(5p^3)/(3m^9n^6)`

Explanation:

`x^-1=1/x`. For example:

`2^2=4`
`2^1=2`
`2^0=1`
Note that for every one the exponent goes down, the result is divided by two. Following this pattern gives us:
`2^-1=1/2`

Applying this to the problem gives us

`((12m^2n^3p^-9)/(20m^-7n^-3p^-6))^-1=(20m^-7n^-3p^-6)/(12m^2n^3p^-9)`

Simplifying each individual exponent gives us

`(20p^(9-6))/(12m^(2+7)n^(3+3))=(20p^3)/(12m^9n^6)`

Because `a^x*a^y=a^(x+y)`

Finally, take out the common factors of the coefficients giving us:

`(20p^3)/(12m^9n^6)=(5p^3)/(3m^9n^6)`, which is the final result