To simplify the expression [tex]\(\frac{5 r^3 t^7}{6 r^5 t^7}\)[/tex], follow these steps:
1. Separate the Coefficients and Variables:
[tex]\[
\frac{5 r^3 t^7}{6 r^5 t^7} = \frac{5}{6} \cdot \frac{r^3}{r^5} \cdot \frac{t^7}{t^7}
\][/tex]
2. Simplify the Coefficient:
[tex]\[
\frac{5}{6}
\][/tex]
3. Simplify the [tex]\(r\)[/tex] Terms:
[tex]\[
\frac{r^3}{r^5} = r^{3-5} = r^{-2}
\][/tex]
4. Simplify the [tex]\(t\)[/tex] Terms:
Since [tex]\(t^7\)[/tex] in the numerator and denominator are the same, they cancel out:
[tex]\[
\frac{t^7}{t^7} = 1
\][/tex]
5. Combine the Simplified Parts:
[tex]\[
\frac{5}{6} \cdot r^{-2} \cdot 1 = \frac{5}{6} \cdot \frac{1}{r^2} = \frac{5}{6 r^2}
\][/tex]
So, the simplified expression is:
[tex]\[
\frac{5}{6 r^2}
\][/tex]
Thus, the correct answer is:
[tex]\(\boxed{\frac{5}{6 r^2}}\)[/tex].
