Answer :
Let's simplify the expression [tex]\(4x^6 u^{-2} \cdot 9w^6 x^9 \cdot 2u w^{-8}\)[/tex] step by step:
1. Combine the Coefficients:
- The coefficients in the expression are [tex]\(4\)[/tex], [tex]\(9\)[/tex], and [tex]\(2\)[/tex].
- Multiply these coefficients together:
[tex]\[
4 \times 9 \times 2 = 72
\][/tex]
2. Simplify the [tex]\(x\)[/tex] terms:
- We have [tex]\(x^6\)[/tex] and [tex]\(x^9\)[/tex].
- Combine these by adding their exponents:
[tex]\[
x^{6 + 9} = x^{15}
\][/tex]
3. Simplify the [tex]\(u\)[/tex] terms:
- We have [tex]\(u^{-2}\)[/tex] and [tex]\(u^1\)[/tex].
- Combine these by adding their exponents:
[tex]\[
u^{-2 + 1} = u^{-1}
\][/tex]
4. Simplify the [tex]\(w\)[/tex] terms:
- We have [tex]\(w^6\)[/tex] and [tex]\(w^{-8}\)[/tex].
- Combine these by adding their exponents:
[tex]\[
w^{6 - 8} = w^{-2}
\][/tex]
5. Combine All Parts and Convert to Positive Exponents:
- The expression becomes [tex]\(72x^{15}u^{-1}w^{-2}\)[/tex].
- To express with positive exponents, rewrite as:
[tex]\[
72x^{15} \cdot \frac{1}{u} \cdot \frac{1}{w^2}
\][/tex]
- This simplifies to:
[tex]\[
\frac{72x^{15}}{u w^2}
\][/tex]
Therefore, the simplified expression with positive exponents is [tex]\(\frac{72x^{15}}{u w^2}\)[/tex].
1. Combine the Coefficients:
- The coefficients in the expression are [tex]\(4\)[/tex], [tex]\(9\)[/tex], and [tex]\(2\)[/tex].
- Multiply these coefficients together:
[tex]\[
4 \times 9 \times 2 = 72
\][/tex]
2. Simplify the [tex]\(x\)[/tex] terms:
- We have [tex]\(x^6\)[/tex] and [tex]\(x^9\)[/tex].
- Combine these by adding their exponents:
[tex]\[
x^{6 + 9} = x^{15}
\][/tex]
3. Simplify the [tex]\(u\)[/tex] terms:
- We have [tex]\(u^{-2}\)[/tex] and [tex]\(u^1\)[/tex].
- Combine these by adding their exponents:
[tex]\[
u^{-2 + 1} = u^{-1}
\][/tex]
4. Simplify the [tex]\(w\)[/tex] terms:
- We have [tex]\(w^6\)[/tex] and [tex]\(w^{-8}\)[/tex].
- Combine these by adding their exponents:
[tex]\[
w^{6 - 8} = w^{-2}
\][/tex]
5. Combine All Parts and Convert to Positive Exponents:
- The expression becomes [tex]\(72x^{15}u^{-1}w^{-2}\)[/tex].
- To express with positive exponents, rewrite as:
[tex]\[
72x^{15} \cdot \frac{1}{u} \cdot \frac{1}{w^2}
\][/tex]
- This simplifies to:
[tex]\[
\frac{72x^{15}}{u w^2}
\][/tex]
Therefore, the simplified expression with positive exponents is [tex]\(\frac{72x^{15}}{u w^2}\)[/tex].
