Question
Simplify this expression using the Quotient Rule of Integer Exponents: t to the 400th power/t to the 100th power .(1 point)
Responses
t to the 300th power
t to the 500th power
300
t to the 4th power
Responses
t to the 300th power
t to the 500th power
300
t to the 4th power
Answers
GPT-4o mini
To simplify the expression \( \frac{t^{400}}{t^{100}} \) using the Quotient Rule of Integer Exponents, we can apply the rule which states that:
\[
\frac{a^m}{a^n} = a^{m-n}
\]
In this case, \( m = 400 \) and \( n = 100 \). Therefore, we can calculate:
\[
\frac{t^{400}}{t^{100}} = t^{400 - 100} = t^{300}
\]
So, the simplified expression is \( t^{300} \).
The correct response is:
**t to the 300th power**
\[
\frac{a^m}{a^n} = a^{m-n}
\]
In this case, \( m = 400 \) and \( n = 100 \). Therefore, we can calculate:
\[
\frac{t^{400}}{t^{100}} = t^{400 - 100} = t^{300}
\]
So, the simplified expression is \( t^{300} \).
The correct response is:
**t to the 300th power**