Question

simplifying rational expressions
what is the simplified form of \\(\frac{-24m^5n^4}{8m^{-7}n^{-3}}\\)? assume \\(m \
eq 0, n \
eq 0\\).
\\(-3m^{12}n^6\\)
\\(-\frac{3n^2}{m^2}\\)
\\(3m^{35}n^8\\)
\\(\frac{3}{m^{35}n^8}\\)

Explanation:

Step1: Split coefficients and variables

$\frac{-24m^5n^4}{8m^{-7}n^{-2}} = \frac{-24}{8} \times \frac{m^5}{m^{-7}} \times \frac{n^4}{n^{-2}}$

Step2: Simplify coefficient fraction

$\frac{-24}{8} = -3$

Step3: Simplify $m$ terms (subtract exponents)

$\frac{m^5}{m^{-7}} = m^{5 - (-7)} = m^{12}$

Step4: Simplify $n$ terms (subtract exponents)

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

Step5: Combine all simplified parts

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

Answer:

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