Question

Solve: (x?)6=x48\left(x^?\right)^{6}=x^{48}(x
?
)
6
=x
48

Answer 1

To solve the equation \((x^?)^6 = x^{48}\), we start by using the property of exponents which states that \((a^m)^n = a^{m \cdot n}\).

Let’s denote the exponent \(? = a\). Then, we can rewrite the equation as:

\[
(x^a)^6 = x^{48}
\]

Applying the property of exponents:

\[
x^{a \cdot 6} = x^{48}
\]

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

\[
a \cdot 6 = 48
\]

Now, let's solve for \(a\):

\[
a = \frac{48}{6}
\]
\[
a = 8
\]

Therefore, \(? = 8\). So, the final solution is:

\[
? = 8
\]