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

Question

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19
4
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9
.(1 point)

Answer 1

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:

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

Answer 2

bot can you put it together?

Answer 3

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.