Question
Simplify this expression using the Quotient Rule of Integer Exponents: t400t100
.(1 point)
Responses
t500
t superscript 500 baseline
300
300
t300
t superscript 300 baseline
t4
.(1 point)
Responses
t500
t superscript 500 baseline
300
300
t300
t superscript 300 baseline
t4
Answers
GPT-4o mini
To simplify the expression \( t^{400} \cdot t^{100} \) using the Quotient Rule of Integer Exponents, we apply the Product Rule of Integer Exponents, which states that when multiplying two powers with the same base, you add their exponents.
So, we have:
\[
t^{400} \cdot t^{100} = t^{400 + 100} = t^{500}
\]
Therefore, the simplified expression is:
**t500 (or \( t^{500} \))**.
So, we have:
\[
t^{400} \cdot t^{100} = t^{400 + 100} = t^{500}
\]
Therefore, the simplified expression is:
**t500 (or \( t^{500} \))**.