2. $$ \frac{-12 m^{6} n^{-4} p^{2}}{3 m^{2} n^{-6} p^{3}} $$

Question

UpStudy AI · Accepted Answer

To simplify the expression:

$$
\frac{-12 m^{6} n^{-4} p^{2}}{3 m^{2} n^{-6} p^{3}}
$$

**Step 1: Simplify the coefficients**

$$
\frac{-12}{3} = -4
$$

**Step 2: Simplify each variable by subtracting the exponents in the denominator from those in the numerator**

- For $$ m $$:
  $$
  m^{6} / m^{2} = m^{6-2} = m^{4}
  $$

- For $$ n $$:
  $$
  n^{-4} / n^{-6} = n^{-4 - (-6)} = n^{2}
  $$

- For $$ p $$:
  $$
  p^{2} / p^{3} = p^{2-3} = p^{-1} = \frac{1}{p}
  $$

**Step 3: Combine all simplified parts**

$$
-4 \times m^{4} \times n^{2} \times \frac{1}{p} = \frac{-4 m^{4} n^{2}}{p}
$$

**Final Simplified Expression:**

$$
\boxed{\displaystyle \frac{-4\,m^{4}n^{2}}{\,p\,}}
$$
$$ \frac{-4m^{4}n^{2}}{p} $$

2. \( \frac{-12 m^{6} n^{-4} p^{2}}{3 m^{2} n^{-6} p^{3}} \)