Let's simplify the expression step-by-step:
[tex]\[
2 w^3 x^{-6} \cdot 4 u x^2 \cdot 9 u^{-2} w^5
\][/tex]
1. Combine the coefficients:
- Multiply the numerical coefficients: [tex]\(2 \cdot 4 \cdot 9 = 72\)[/tex].
2. Combine the exponents for each variable:
- For [tex]\(w\)[/tex]:
[tex]\[
w^3 \cdot w^5 = w^{3+5} = w^8
\][/tex]
- For [tex]\(x\)[/tex]:
[tex]\[
x^{-6} \cdot x^2 = x^{-6+2} = x^{-4}
\][/tex]
- For [tex]\(u\)[/tex]:
[tex]\[
u \cdot u^{-2} = u^{1 + (-2)} = u^{1-2} = u^{-1}
\][/tex]
3. Express the final answer with positive exponents:
- [tex]\(x^{-4}\)[/tex] remains as [tex]\(x^{-4}\)[/tex] since we can include negative exponents.
- [tex]\(u^{-1}\)[/tex] remains as [tex]\(u^{-1}\)[/tex] since we can include negative exponents.
Putting it all together, the simplified expression is:
[tex]\[
72 w^8 x^{-4} u^{-1}
\][/tex]
