Question

Simplify this expression using the Quotient Rule of Integer Exponents: t400t100

Answer 1

To simplify the expression \( t^{400} t^{100} \) using the Quotient Rule of Integer Exponents, we actually use the Product Rule instead, since we are multiplying two expressions with the same base.

The Product Rule states that when you multiply two expressions with the same base, you add their exponents:

\[
a^m \cdot a^n = a^{m+n}
\]

Applying this rule to your expression:

\[
t^{400} t^{100} = t^{400 + 100} = t^{500}
\]

So, the simplified expression is:

\[
t^{500}
\]