Use the Power Rule of Exponents to create a simplified equivalent expression for (19^4)^9

Question

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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, calculating \(4 \cdot 9\):

\[ 4 \cdot 9 = 36 \]

Thus, we have:

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

The simplified equivalent expression is:

\[ \boxed{19^{36}} \]