Question

simplify.
$(8^{3})^{7} = 8^{n}$
$n = \square$
done

Explanation:

Step1: Apply power of a power rule

To simplify \((8^{3})^{7}\), we use the power of a power rule, which states that \((a^{m})^{n}=a^{m\times n}\). Here, \(a = 8\), \(m = 3\), and \(n = 7\). So we calculate \(3\times7\).
\(3\times7 = 21\)
So \((8^{3})^{7}=8^{21}\).

Step2: Determine the value of \(n\)

Since \((8^{3})^{7}=8^{n}\) and we found that \((8^{3})^{7}=8^{21}\), by the equality of exponents when the bases are the same, we can see that \(n = 21\).

Answer:

\(21\)