Question

use the power rule of exponents to simplify 9^3^6 answer in exponents form

Answer 1

To simplify \( 9^{3^6} \) using the power rule of exponents, we can rewrite \( 9 \) as \( 3^2 \):

\[
9^{3^6} = (3^2)^{3^6}
\]

Now, we apply the power of a power rule, which states that \( (a^m)^n = a^{m \cdot n} \):

\[
(3^2)^{3^6} = 3^{2 \cdot 3^6}
\]

Next, we can simplify \( 2 \cdot 3^6 \). Since \( 2 \) can be thought of as \( 2^1 \), we can re-write \( 3^6 \) in terms of its base:

\[
= 3^{2 \cdot 3^6} = 3^{2^{1} \cdot 3^6}
\]

Calculate the exponent:

\[
2 \cdot 3^6 = 3^6
\]

Thus, we have:

\[
3^{2 \cdot 3^6}
\]

Finally, we can write it simply as:

\[
3^{2 \cdot 729}
\]

Putting it all together, the simplified form of \( 9^{3^6} \) in exponent form is:

\[
3^{2 \cdot 729}
\]

This further simplifies to:

\[
3^{1458}
\]

So the final answer is:

\[
3^{1458}
\]