Question
Use the Power Rule of Exponents to create a simplified equivalent expression for (19 rasied to the power of 4) rasied to the power of 9
Answers
Answered by
GPT-4o mini
To simplify the expression \((19^4)^9\) using the Power Rule of Exponents, we apply the rule which states that \((a^m)^n = a^{m \cdot n}\).
In this case:
\[
(19^4)^9 = 19^{4 \cdot 9}
\]
Now, calculate \(4 \cdot 9\):
\[
4 \cdot 9 = 36
\]
So, we can simplify the expression to:
\[
(19^4)^9 = 19^{36}
\]
Thus, the simplified equivalent expression is:
\[
19^{36}
\]
In this case:
\[
(19^4)^9 = 19^{4 \cdot 9}
\]
Now, calculate \(4 \cdot 9\):
\[
4 \cdot 9 = 36
\]
So, we can simplify the expression to:
\[
(19^4)^9 = 19^{36}
\]
Thus, the simplified equivalent expression is:
\[
19^{36}
\]