Simplify. Express your answer using positive exponents. $$ 2 u^{3} v w^{9} \cdot 8 u^{5} v w \cdot 6 u^{2} v^{2} w^{2} $$

Question

UpStudy AI · Accepted Answer

We start with the expression:

$$
2 u^{3} v w^{9} \cdot 8 u^{5} v w \cdot 6 u^{2} v^{2} w^{2}
$$

**Step 1. Multiply the numerical coefficients:**

$$
2 \cdot 8 \cdot 6 = 96
$$

**Step 2. Combine the like variables using the law of exponents:**

For $$ u $$:

$$
u^{3} \cdot u^{5} \cdot u^{2} = u^{3+5+2} = u^{10}
$$

For $$ v $$:

$$
v \cdot v \cdot v^{2} = v^{1+1+2} = v^{4}
$$

For $$ w $$:

$$
w^{9} \cdot w \cdot w^{2} = w^{9+1+2} = w^{12}
$$

**Step 3. Write the simplified expression:**

$$
96 u^{10} v^4 w^{12}
$$
$$ 96 u^{10} v^{4} w^{12} $$

Simplify. Express your answer using positive exponents. \( 2 u^{3} v w^{9} \cdot 8 u^{5} v w \cdot 6 u^{2} v^{2} w^{2} \)