Question

Simplify this expression using the Quotient
Rule of Integer Exponents: . (1 point)
t
400
t
100
t
4
t
300
300
t
500

Answer 1

To simplify the expression \( \frac{t^{400} \cdot t^{100} \cdot t^{4}}{t^{300} \cdot t^{500}} \) using the Quotient Rule of Integer Exponents, we can follow these steps:

1. Combine the exponents in the numerator and the denominator:
- For the numerator:
\[
t^{400} \cdot t^{100} \cdot t^{4} = t^{400 + 100 + 4} = t^{504}
\]
- For the denominator:
\[
t^{300} \cdot t^{500} = t^{300 + 500} = t^{800}
\]

2. Now the expression looks like:
\[
\frac{t^{504}}{t^{800}}
\]

3. Applying the Quotient Rule, which states that \( \frac{a^m}{a^n} = a^{m-n} \), we get:
\[
t^{504 - 800} = t^{-296}
\]

4. The final simplified expression is:
\[
t^{-296}
\]

If you want to express it positively, you can also write it as:
\[
\frac{1}{t^{296}}
\]

So, the simplified expression is \( t^{-296} \) or \( \frac{1}{t^{296}} \).