Question

Solve: (p4)?=p24\left(p^{4}\right)^?=p^{24}(p
4
)
?
=p
24

Answer 1

To solve the equation \((p^4)? = p^{24}\), we need to determine the value of the question mark \((?)\).

Let's denote the unknown value as \(x\). Therefore, we can rewrite the equation:

\[
(p^4)^x = p^{24}
\]

Using the exponentiation rule \((a^m)^n = a^{m \cdot n}\), we can simplify the left side:

\[
p^{4x} = p^{24}
\]

Since the bases are the same, we can set the exponents equal to each other:

\[
4x = 24
\]

Now, solve for \(x\):

\[
x = \frac{24}{4} = 6
\]

Thus, the value of the question mark \((?)\) is:

\[
\boxed{6}
\]