Question
Eighth grade C. 18 Multiply and divide powersi varlable bases 85 P \[ \begin{array}{l}\text { 41) Simplify. Express your answer using positive exponents. } \\ 2 u^{3} v w^{9} \cdot 8 u^{5} v w \cdot 6 u^{2} v^{2} w^{2}\end{array} \]
Ask by Bowen Huang. in the United States
Mar 08,2025
Upstudy AI Solution
Tutor-Verified Answer
Answer
The simplified expression is \( 96u^{10}v^4w^{12} \).
Solution
First, multiply the numerical coefficients:
\[
2 \cdot 8 \cdot 6 = 96
\]
Next, add the exponents of \( u \):
\[
u^3 \cdot u^5 \cdot u^2 = u^{3+5+2} = u^{10}
\]
Then, add the exponents of \( v \):
\[
v \cdot v \cdot v^2 = v^{1+1+2} = v^4
\]
Finally, add the exponents of \( w \):
\[
w^9 \cdot w \cdot w^2 = w^{9+1+2} = w^{12}
\]
Putting it all together, the simplified expression is:
\[
96u^{10}v^4w^{12}
\]
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Simplify this solution Mind Expander
To simplify \(2 u^{3} v w^{9} \cdot 8 u^{5} v w \cdot 6 u^{2} v^{2} w^{2}\), start by multiplying the coefficients first: \(2 \cdot 8 \cdot 6 = 96\). Next, combine the like bases for \(u\), \(v\), and \(w\): - For \(u\): \(u^3 \cdot u^5 \cdot u^2 = u^{3+5+2} = u^{10}\) - For \(v\): \(v^1 \cdot v^1 \cdot v^2 = v^{1+1+2} = v^{4}\) - For \(w\): \(w^9 \cdot w^1 \cdot w^2 = w^{9+1+2} = w^{12}\) Now, put it all together: \(96 u^{10} v^{4} w^{12}\). Final answer: \(96 u^{10} v^{4} w^{12}\).
