To solve the expression [tex]\( -27 s^3 t \times \frac{2 t u^4}{3 s^2 t u^2} \)[/tex], follow these steps:
1. Separate the coefficients and variables:
- Coefficient of the first term: [tex]\(-27\)[/tex]
- Coefficient of the second term: [tex]\(\frac{2}{3}\)[/tex]
- Variables and their exponents in the first term: [tex]\(s^3 t\)[/tex]
- Variables and their exponents in the second term: [tex]\(\frac{t u^4}{s^2 t u^2}\)[/tex]
2. Multiply the coefficients separately:
[tex]\[
-27 \times \frac{2}{3} = -27 \times \frac{2}{3} = -18
\][/tex]
3. Combine the variables with the same bases by adding and subtracting their exponents:
- For [tex]\(s\)[/tex]:
[tex]\[
s^3 \times s^{-2} = s^{3 + (-2)} = s^1
\][/tex]
- For [tex]\(t\)[/tex]:
[tex]\[
t \times t^{-1} \times t = t^{1-1+1} = t^2
\][/tex]
- For [tex]\(u\)[/tex]:
[tex]\[
\frac{u^4}{u^2} = u^{4-2} = u^2
\][/tex]
4. Combine results:
The coefficient is [tex]\(-18\)[/tex], and the resulting exponents are [tex]\(s^1\)[/tex], [tex]\(t^2\)[/tex], and [tex]\(u^2\)[/tex].
Putting everything together, the expression simplifies to:
[tex]\[
-18 s^1 t^2 u^2
\][/tex]
Or simply:
[tex]\[
-18 s t^2 u^2
\][/tex]
So, the final result of the expression [tex]\( -27 s^3 t \times \frac{2 t u^4}{3 s^2 t u^2} \)[/tex] is:
[tex]\[
-18 s t^2 u^2
\][/tex]
