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

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

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

Answer

Answer:

A. $\frac{n^{10}}{16m^{6}}$

Explanation:

Step1: Apply power - of - a - quotient rule

$(\frac{4mn}{m^{-2}n^{6}})^{-2}=\frac{(4mn)^{-2}}{(m^{-2}n^{6})^{-2}}$

Step2: Apply power - of - a - product rule

$(4mn)^{-2}=4^{-2}m^{-2}n^{-2}=\frac{1}{16}m^{-2}n^{-2}$ and $(m^{-2}n^{6})^{-2}=m^{4}n^{-12}$

Step3: Divide the two expressions

$\frac{\frac{1}{16}m^{-2}n^{-2}}{m^{4}n^{-12}}=\frac{1}{16}m^{-2 - 4}n^{-2+12}$

Step4: Simplify the exponents

$\frac{1}{16}m^{-6}n^{10}=\frac{n^{10}}{16m^{6}}$