Question

Simplify. Express your answer using positive exponents.
4r4st2
2r9s8t

Answer 1

To simplify the expression \(\frac{4r^4s^2}{2r^9s^8t}\), we can follow these steps:

1. **Divide the coefficients**:
\[
\frac{4}{2} = 2
\]

2. **Simplify the \(r\) terms**:
\[
\frac{r^4}{r^9} = r^{4-9} = r^{-5}
\]

3. **Simplify the \(s\) terms**:
\[
\frac{s^2}{s^8} = s^{2-8} = s^{-6}
\]

4. **The \(t\) term stays in the denominator**:
\[
t
\]

Now combining all results:
\[
\frac{4r^4s^2}{2r^9s^8t} = 2r^{-5}s^{-6}t^{-1}
\]

To express the answer using positive exponents, we can rewrite this as:
\[
\frac{2}{r^5s^6t}
\]

Thus, the simplified expression is:
\[
\frac{2}{r^5s^6t}
\]