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}#?

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Answer 1 · 2018-05-16T00:04:42

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

#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