To simplify the expression:

\[
\frac{r^8 s^{-5} t^0}{r^0 s^{-5} t^6}
\]

### Step-by-step solution:

1. **Simplify \( t^0 \)**:
   Since \( t^0 = 1 \), we can eliminate \( t^0 \) from the numerator:
   \[
   \frac{r^8 s^{-5}}{r^0 s^{-5} t^6}
   \]

2. **Simplify each variable by subtracting exponents**:
   - For \( r \), subtract the exponents:
     \[
     \frac{r^8}{r^0} = r^{8 - 0} = r^8
     \]
   
   - For \( s \), subtract the exponents:
     \[
     \frac{s^{-5}}{s^{-5}} = s^{-5 - (-5)} = s^0 = 1
     \]
     So, \( s \) cancels out entirely.

   - For \( t \), since there is no \( t \) in the numerator, just keep \( t^6 \) in the denominator:
     \[
     \frac{1}{t^6}
     \]

### Final simplified expression:
\[
\frac{r^8}{t^6}
\]

Would you like more details on any of these steps?

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Here are 5 related questions:
1. How do you handle terms like \( t^0 \) and \( r^0 \) in expressions?
2. What happens when both numerator and denominator have the same exponent for a variable?
3. How would you simplify \( \frac{a^m}{a^0} \)?
4. What happens when the exponents cancel out for a variable, like \( s^{-5}/s^{-5} \)?
5. Can you simplify expressions like \( \frac{x^a y^b}{x^c y^d} \)?

**Tip**: When you encounter \( x^0 \) in an expression, remember it always equals 1 as long as \( x \neq 0 \).

Learn how to simplify the exponential expression r^8s^-5t^0 / r^0s^-5t^6 with a step-by-step breakdown. This problem covers key algebraic concepts such as exponent rules and the simplification of rational expressions. Suitable for students in Grades 8-10.

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