what is the simplified form of $\frac{-24m^{5}n^{4}}{8m^{-7}n^{-2}}$? assume $m\neq0,n\neq0$.\n$\frac{3}{m^{3…

Explanation:

Step1: Divide the coefficients

Divide -24 by 8: $\frac{-24}{8}=-3$.

Step2: Use the quotient - rule for exponents with the same base

For the $m$ terms, $\frac{m^{5}}{m^{-7}}=m^{5-(-7)} = m^{5 + 7}=m^{12}$ (using the rule $\frac{a^{m}}{a^{n}}=a^{m - n}$).

Step3: Use the quotient - rule for exponents with the same base for $n$ terms

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: $-3\times m^{12}\times n^{6}=-3m^{12}n^{6}$.

Answer:

-3m^{12}n^{6}