Certainly! Let's find the result of the given expression step by step:
We have to divide the expression [tex]\(\frac{18 r^4 s^5 t^6}{-3 r^2 s t^3}\)[/tex].
1. Divide the numerical coefficients:
[tex]\[
\frac{18}{-3} = -6
\][/tex]
2. Simplify the powers of [tex]\(r\)[/tex]:
In the numerator, the power of [tex]\(r\)[/tex] is 4, and in the denominator, the power of [tex]\(r\)[/tex] is 2.
[tex]\[
r^{4 - 2} = r^2
\][/tex]
3. Simplify the powers of [tex]\(s\)[/tex]:
In the numerator, the power of [tex]\(s\)[/tex] is 5, and in the denominator, the power of [tex]\(s\)[/tex] is 1.
[tex]\[
s^{5 - 1} = s^4
\][/tex]
4. Simplify the powers of [tex]\(t\)[/tex]:
In the numerator, the power of [tex]\(t\)[/tex] is 6, and in the denominator, the power of [tex]\(t\)[/tex] is 3.
[tex]\[
t^{6 - 3} = t^3
\][/tex]
Putting it all together, we get:
[tex]\[
\frac{18 r^4 s^5 t^6}{-3 r^2 s t^3} = -6 r^2 s^4 t^3
\][/tex]
Therefore, the correct answer is:
A. [tex]\(-6 r^2 s^4 t^3\)[/tex]
