what is the quotient $\frac{2m^{9}n^{4}}{-4m^{-3}n^{-2}}$ in simplest form? assume $m\neq0,n\neq0$.\n$-\frac{…

what is the quotient $\frac{2m^{9}n^{4}}{-4m^{-3}n^{-2}}$ in simplest form? assume $m\neq0,n\neq0$.\n$-\frac{m^{12}n^{6}}{2}$\n$-\frac{m^{27}n^{8}}{2}$\n$6m^{12}n^{6}$\n$8m^{12}n^{6}$

what is the quotient $\frac{2m^{9}n^{4}}{-4m^{-3}n^{-2}}$ in simplest form? assume $m\neq0,n\neq0$.\n$-\frac{m^{12}n^{6}}{2}$\n$-\frac{m^{27}n^{8}}{2}$\n$6m^{12}n^{6}$\n$8m^{12}n^{6}$

Answer

Explanation:

Step1: Divide the coefficients

Divide 2 by - 4, $\frac{2}{-4}=-\frac{1}{2}$.

Step2: Use the quotient - rule of exponents for $m$

For the $m$ terms, $\frac{m^{9}}{m^{-3}}=m^{9-(-3)}=m^{9 + 3}=m^{12}$ (using the rule $\frac{a^{m}}{a^{n}}=a^{m - n}$).

Step3: Use the quotient - rule of exponents for $n$

For the $n$ terms, $\frac{n^{4}}{n^{-2}}=n^{4-(-2)}=n^{4 + 2}=n^{6}$ (using the rule $\frac{a^{m}}{a^{n}}=a^{m - n}$).

Step4: Combine the results

Multiply the results from steps 1 - 3: $-\frac{1}{2}m^{12}n^{6}=-\frac{m^{12}n^{6}}{2}$.

Answer:

$-\frac{m^{12}n^{6}}{2}$