Question

use the power rule of exponents to create a simplified equivalent expression for (19 to the power of 4)to the power of 9

Answer 1

To simplify the expression \((19^4)^9\) using the power rule of exponents, which states that \((a^m)^n = a^{m \cdot n}\), we can apply this rule as follows:

\[
(19^4)^9 = 19^{4 \cdot 9}
\]

Now, we calculate \(4 \cdot 9\):

\[
4 \cdot 9 = 36
\]

So, we have:

\[
(19^4)^9 = 19^{36}
\]

Thus, the simplified equivalent expression is:

\[
19^{36}
\]