The expression that is equivalent to the given statement was reduced.
The given expression is:
[tex]\frac{(3m^{-2}n)^{-3} }{6mn^{-2} }[/tex]
Some important power rules are:
[tex](ab)^n=a^nb^n[/tex]
[tex](a^{m} )^n=a^{mn}[/tex]
[tex]a^m.a^n=a^{m+n}[/tex]
[tex]\frac{a^m}{a^n} =a^{m-n}[/tex]
[tex]a^{-m} =\frac{1}{a^m}[/tex]
So, the given expression can be written as:
[tex]\frac{3^{-3} m^{6} n^{-3} }{6mn^{-2} }[/tex]
=[tex](\frac{3^{-3} }{6} )*(\frac{m^{6} }{m} )*(\frac{n^{-3} }{n^{-2} } )[/tex]
=[tex](\frac{1}{3^{3} *6} )*m^{5} *(\frac{1}{n^{3} *n^{-2} } )[/tex]
=[tex]\frac{m^5}{162n}[/tex]
Hence, the expression that is equivalent to the given statement was reduced.
To get more about power rules visit:
https://brainly.com/question/819893
