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To simplify the given expression \( t^{-4} t^{-1} \) and express the result with positive exponents:

1. Apply the rule of exponents: \( a^m a^n = a^{m+n} \), which means we can add the exponents when multiplying terms with the same base.

\[
t^{-4} t^{-1} = t^{-4 + (-1)} = t^{-5}
\]

2. To express the result with a positive exponent, recall that \( t^{-n} = \frac{1}{t^n} \).

\[
t^{-5} = \frac{1}{t^5}
\]

Thus, the simplified expression is:

\[
\frac{1}{t^5}
\]

Would you like more details or have any questions? 

Here are 5 related questions to explore this concept further:
1. How do you simplify \( t^3 t^{-2} \)?
2. What happens when you multiply terms with different bases but the same exponent, like \( a^3 b^3 \)?
3. How do you simplify \( (t^2)^3 \)?
4. What is the result of dividing \( t^7 \) by \( t^2 \)?
5. How do you handle expressions with both negative exponents and fractions?

**Tip:** Remember that negative exponents indicate reciprocal relationships—so \( a^{-n} \) means \( \frac{1}{a^n} \).

Simplify the following expression: t^{-4} t^{-1}. Write your answer with positive exponents.

Learn how to simplify the expression t^{-4} t^{-1} and express the result with positive exponents. This problem covers key concepts in algebra, including exponent rules. Suitable for students in Grades 8-10.

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