Question
Simplify. Express your answer using positive exponents. \( 2 u^{3} v w^{9} \cdot 8 u^{5} v w \cdot 6 u^{2} v^{2} w^{2} \)
Ask by Alexander Donnelly. in the United States
Mar 08,2025
Upstudy AI Solution
Tutor-Verified Answer
Answer
\( 96 u^{10} v^{4} w^{12} \)
Solution
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:**
\[
96 u^{10} v^4 w^{12}
\]
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Simplify this solution Bonus Knowledge
To simplify the expression \( 2 u^{3} v w^{9} \cdot 8 u^{5} v w \cdot 6 u^{2} v^{2} w^{2} \), start by multiplying the coefficients together: \( 2 \cdot 8 \cdot 6 = 96 \). Next, combine the variables using the rule of exponents (add the exponents for like bases): - 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 \( w \): \( w^{9} \cdot w \cdot w^{2} = w^{9+1+2} = w^{12} \) Now, combine all of it together: The simplified expression is \( 96 u^{10} v^{4} w^{12} \).
