Question
Simplify and write the answer with positive exponents only. \( \frac{t^{2}}{t^{7}}=\square \)
Ask by Weston Wells. in the United States
Jan 27,2025
Real Tutor Solution
Tutor-Verified Answer
Answer
\[
\frac{1}{t^{5}}
\]
Solution
To simplify the expression \( \frac{t^{2}}{t^{7}} \) and ensure the result has only positive exponents, follow these steps:
1. **Subtract the Exponents:**
When you divide expressions with the same base, you subtract the exponents:
\[
\frac{t^{2}}{t^{7}} = t^{2 - 7} = t^{-5}
\]
2. **Rewrite with Positive Exponents:**
A negative exponent indicates the reciprocal of the base raised to the positive exponent. Thus,
\[
t^{-5} = \frac{1}{t^{5}}
\]
**Final Answer:**
\[
\frac{1}{t^{5}}
\]
Reviewed and approved by the UpStudy tutoring team
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Simplify this solution Mind Expander
To simplify \( \frac{t^{2}}{t^{7}} \), you subtract the exponents of \( t \). So, you get: \[ t^{2-7} = t^{-5} \] To express this with a positive exponent, you can rewrite it as: \[ \frac{1}{t^{5}} \] So the answer is \( \frac{1}{t^{5}} \).
