Questions: What is the quotient 2m^9 n^4/-4m^-3 n^-2 in simplest form? Assume m ≠ 0, n ≠ 0. -m^27 n^8/2 -m^12 n^6/2 8m^12 n^6 6m^12 n^6

Transcript text: What is the quotient $\frac{2 m^{9} n^{4}}{-4 m^{-3} n^{-2}}$ in simplest form? Assume $m \neq 0, n \neq 0$. $-\frac{m^{27} n^{8}}{2}$ $-\frac{m^{12} n^{6}}{2}$ $8 m^{12} n^{6}$ $6 m^{12} n^{6}$

Solution

Solution Steps

Step 1: Simplify the Expression

The given expression is:

\[ \frac{2 m^{9} n^{4}}{-4 m^{-3} n^{-2}} \]

First, simplify the coefficients:

\[ \frac{2}{-4} = -\frac{1}{2} \]

Next, simplify the powers of $m$ and $n$ using the laws of exponents:

\[ m^{9} \div m^{-3} = m^{9 - (-3)} = m^{9 + 3} = m^{12} \]

\[ n^{4} \div n^{-2} = n^{4 - (-2)} = n^{4 + 2} = n^{6} \]

Step 2: Combine the Simplified Parts

Combine the simplified coefficient and the simplified powers of $m$ and $n$:

\[ -\frac{1}{2} \cdot m^{12} \cdot n^{6} = -\frac{m^{12} n^{6}}{2} \]

Final Answer

The simplest form of the given expression is:

\[ \boxed{-\frac{m^{12} n^{6}}{2}} \]

Thus, the answer is the second option:

\[ \boxed{-\frac{m^{12} n^{6}}{2}} \]

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