To solve the expression [tex]\(\frac{18 r^4 s^5 t^6}{-3 r^2 s t^3}\)[/tex], follow these steps:
1. Divide the coefficients:
[tex]\[
\frac{18}{-3} = -6
\][/tex]
2. Simplify the [tex]\(r\)[/tex] terms:
The exponent rule for division states that you subtract the exponents when dividing like bases. Thus,
[tex]\[
\frac{r^4}{r^2} = r^{4-2} = r^2
\][/tex]
3. Simplify the [tex]\(s\)[/tex] terms:
Similarly, apply the exponent rule:
[tex]\[
\frac{s^5}{s} = s^{5-1} = s^4
\][/tex]
4. Simplify the [tex]\(t\)[/tex] terms:
Again, apply the exponent rule:
[tex]\[
\frac{t^6}{t^3} = t^{6-3} = t^3
\][/tex]
5. Combine all simplified terms:
Putting everything together, we get:
[tex]\[
-6 \cdot r^2 \cdot s^4 \cdot t^3
\][/tex]
Thus, the final result is:
[tex]\[ -6 r^2 s^4 t^3 \][/tex]
Therefore, the correct answer is:
B. [tex]\(-6 r^2 s^4 t^3\)[/tex]
