Simplify this expression using the Quotient Rule of Integer Exponents: t(400)/t(100)

Question

.(1 point)
Responses

t(500)
t superscript 500 baseline

300
300

t(4)
t superscript 4 baseline

t(300)

Answer 1

To simplify the expression \( \frac{t(400)}{t(100)} \) using the Quotient Rule of Integer Exponents, we apply the rule that states \( \frac{a^m}{a^n} = a^{m-n} \).

Here, we can treat \( t(400) \) as \( t^{400} \) and \( t(100) \) as \( t^{100} \).

Using the Quotient Rule:

\[ \frac{t^{400}}{t^{100}} = t^{400 - 100} = t^{300}. \]

Thus, the simplified expression is:

t(300).