(9^2)^4

1 answer

To evaluate \((9^2)^4\), you can use the power of a power property of exponents, which states that \((a^m)^n = a^{m \cdot n}\).

Here, \(a = 9\), \(m = 2\), and \(n = 4\).

So, we have:

\[ (9^2)^4 = 9^{2 \cdot 4} = 9^8 \]

Next, we can calculate \(9^8\):

\[ 9^8 = (3^2)^8 = 3^{2 \cdot 8} = 3^{16} \]

To find \(9^8\) directly, you can calculate it as:

\[ 9^8 = 9 \times 9 \times 9 \times 9 \times 9 \times 9 \times 9 \times 9 \]

This equals \(43046721\).

So,

\[ (9^2)^4 = 9^8 = 43046721. \]

Thus, the final answer is:

\[ \boxed{43046721} \]