Use the Power Rule of Exponents to create a simplified equivalent expression for (194)9

To simplify the expression \( (194)^9 \) using the Power Rule of Exponents, we apply the rule which states that \( (a^m)^n = a^{m \cdot n} \).

First, let's factor \( 194 \):

\[
194 = 2 \times 97
\]

Now we can express \( (194)^9 \) as:

\[
(194)^9 = ((2 \times 97)^1)^9
\]

Using the Power Rule, we rewrite it:

\[
(194)^9 = 2^9 \times 97^9
\]

Thus, the simplified equivalent expression for \( (194)^9 \) is:

\[
2^9 \times 97^9
\]

This can also be written as:

\[
(2 \times 97)^9 = 194^9
\]

However, since the expression \( 194^9 \) is the original form, the simplified form remains \( 2^9 \times 97^9 \) for clarity.

So, the final answer is:

\[
2^9 \times 97^9
\]

bot can you put it together?

Certainly!

The simplified equivalent expression for \( (194)^9 \) using the Power Rule of Exponents is:

\[
2^9 \times 97^9
\]

So, putting it all together:

\[
(194)^9 = 2^9 \times 97^9
\]

This is the finalized expression.