which expression is equivalent to $\frac{(3m^{-1}n^{2})^{4}}{(2m^{-2}n)^{3}}$? assume $m\neq0,n\neq0$.\n$2m^{…

which expression is equivalent to $\frac{(3m^{-1}n^{2})^{4}}{(2m^{-2}n)^{3}}$? assume $m\neq0,n\neq0$.\n$2m^{2}n^{5}$\n$\frac{81m^{2}n^{5}}{8}$\n$2m^{2}n^{2}$\n$\frac{81m^{2}n^{2}}{8}$

which expression is equivalent to $\frac{(3m^{-1}n^{2})^{4}}{(2m^{-2}n)^{3}}$? assume $m\neq0,n\neq0$.\n$2m^{2}n^{5}$\n$\frac{81m^{2}n^{5}}{8}$\n$2m^{2}n^{2}$\n$\frac{81m^{2}n^{2}}{8}$

Answer

Explanation:

Step1: Apply power - of - a - power rule

For ((a^m)^n=a^{mn}), we have ((3m^{- 1}n^{2})^{4}=3^{4}m^{-4}n^{8}=81m^{-4}n^{8}) and ((2m^{-2}n)^{3}=2^{3}m^{-6}n^{3}=8m^{-6}n^{3}).

Step2: Divide the two expressions

(\frac{(3m^{-1}n^{2})^{4}}{(2m^{-2}n)^{3}}=\frac{81m^{-4}n^{8}}{8m^{-6}n^{3}}).

Step3: Use the quotient rule (a^m\div a^n=a^{m - n})

(\frac{81}{8}m^{-4-(-6)}n^{8 - 3}=\frac{81}{8}m^{2}n^{5}).

Answer:

(\frac{81m^{2}n^{5}}{8})