which expression is equivalent to $\frac{(2mn)^{4}}{6m^{-3}n^{-2}}$? assume $m\neq0,n\neq0$.\n$\frac{8m^{7}n^…

which expression is equivalent to $\frac{(2mn)^{4}}{6m^{-3}n^{-2}}$? assume $m\neq0,n\neq0$.\n$\frac{8m^{7}n^{6}}{3}$\n$\frac{10m^{7}n^{6}}{3}$\n$\frac{8m^{16}n^{12}}{3}$\n$\frac{m^{4}n^{6}}{3}$

which expression is equivalent to $\frac{(2mn)^{4}}{6m^{-3}n^{-2}}$? assume $m\neq0,n\neq0$.\n$\frac{8m^{7}n^{6}}{3}$\n$\frac{10m^{7}n^{6}}{3}$\n$\frac{8m^{16}n^{12}}{3}$\n$\frac{m^{4}n^{6}}{3}$

Answer

Explanation:

Step1: Expand the numerator

Use the power - of - a - product rule ((ab)^n=a^n b^n). So, ((2mn)^4 = 2^4m^4n^4=16m^4n^4).

Step2: Rewrite the expression

The original expression (\frac{(2mn)^4}{6m^{-3}n^{-2}}) becomes (\frac{16m^4n^4}{6m^{-3}n^{-2}}).

Step3: Use the quotient rule of exponents

The quotient rule is (\frac{a^m}{a^n}=a^{m - n}). So, (\frac{16m^4n^4}{6m^{-3}n^{-2}}=\frac{16}{6}m^{4-(-3)}n^{4-(-2)}).

Step4: Simplify the coefficient and exponents

(\frac{16}{6}=\frac{8}{3}), (m^{4 + 3}=m^7), and (n^{4+2}=n^6). The simplified expression is (\frac{8m^7n^6}{3}).

Answer:

A. (\frac{8m^7n^6}{3})