Select the best answer for the question.

16. What is the result if you divide [tex]$\frac{18 r^4 s^5 t^6}{-3 r^2 s t^3}$[/tex]?

A. [tex]$-6 r^2 s^5 t^3$[/tex]

B. [tex][tex]$6 r^2 s^5 t^3$[/tex][/tex]

C. [tex]$-6 r^2 s^4 t^3$[/tex]

D. [tex]$6 r^2 s^4 t^3$[/tex]



Answer :

To solve the problem [tex]\(\frac{18 r^4 s^5 t^6}{-3 r^2 s t^3}\)[/tex], we need to follow these steps:

1. Divide the coefficients:
[tex]\[ \frac{18}{-3} = -6 \][/tex]

2. Subtract the exponents of [tex]\(r\)[/tex]:
[tex]\[ \frac{r^4}{r^2} = r^{4-2} = r^2 \][/tex]

3. Subtract the exponents of [tex]\(s\)[/tex]:
[tex]\[ \frac{s^5}{s^1} = s^{5-1} = s^4 \][/tex]

4. Subtract the exponents of [tex]\(t\)[/tex]:
[tex]\[ \frac{t^6}{t^3} = t^{6-3} = t^3 \][/tex]

Combining these results, we get:
[tex]\( -6 r^2 s^4 t^3 \)[/tex]

Thus, the best answer is:
C. [tex]\(-6 r^2 s^4 t^3\)[/tex]