19. $$ \left(-18 m^{2} n\right)^{2}\left(-\frac{1}{6} m n^{2}\right) $$

Question

UpStudy AI · Accepted Answer

To simplify the expression:

$$
\left(-18 m^{2} n\right)^{2} \left(-\frac{1}{6} m n^{2}\right)
$$

**Step 1: Square the first part**

$$
\left(-18 m^{2} n\right)^{2} = (-18)^2 \cdot (m^2)^2 \cdot (n)^2 = 324 m^{4} n^{2}
$$

**Step 2: Multiply the squared result by the second part**

$$
324 m^{4} n^{2} \cdot \left(-\frac{1}{6} m n^{2}\right) 
$$

**Step 3: Multiply the coefficients**

$$
324 \times \left(-\frac{1}{6}\right) = -54
$$

**Step 4: Multiply the variables**

$$
m^{4} \times m = m^{5} \quad \text{and} \quad n^{2} \times n^{2} = n^{4}
$$

**Final Result:**

$$
-54 m^{5} n^{4}
$$

**Answer:** $$-54\,m^{5}\,n^{4}$$
$$-54\,m^{5}\,n^{4}$$

19. \( \left(-18 m^{2} n\right)^{2}\left(-\frac{1}{6} m n^{2}\right) \)