Question
Question
Simplify this expression using the Quotient Rule of Integer Exponents: t400t100
.(1 point)
Responses
300
300
t4
t superscript 4 baseline
t300
t superscript 300 baseline
t500
Answers
GPT-4o mini
To simplify the expression \( t^{400} \cdot t^{100} \) using the Quotient Rule of Integer Exponents, we actually should apply the Product Rule of Integer Exponents, since we are multiplying.
The Product Rule states that when you multiply two expressions with the same base, you add the exponents:
\[
t^m \cdot t^n = t^{m+n}
\]
In this case:
\[
t^{400} \cdot t^{100} = t^{400 + 100} = t^{500}
\]
So the simplified expression is \( t^{500} \).
Therefore, the correct answer is:
**t500**
The Product Rule states that when you multiply two expressions with the same base, you add the exponents:
\[
t^m \cdot t^n = t^{m+n}
\]
In this case:
\[
t^{400} \cdot t^{100} = t^{400 + 100} = t^{500}
\]
So the simplified expression is \( t^{500} \).
Therefore, the correct answer is:
**t500**