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]\(-6 r^2 s^4 t^3\)[/tex]

C. [tex]\(6 r^2 s^5 t^3\)[/tex]

D. [tex]\(6 r^2 s^4 t^3\)[/tex]



Answer :

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]