Question

Solve: (x5)?=x40\left(x^{5}\right)^?=x^{40}(x
5
)
?
=x
40

Answer 1

To solve the equation \((x^5)^{?} = x^{40}\), we can use the properties of exponents.

Using the power of a power property, we know that:

\[
(a^m)^n = a^{m \cdot n}
\]

Applying this to our equation:

\[
(x^5)^{?} = x^{5 \cdot ?}
\]

Setting this equal to \(x^{40}\), we have:

\[
x^{5 \cdot ?} = x^{40}
\]

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

\[
5 \cdot ? = 40
\]

Now we can solve for \(?\):

\[
? = \frac{40}{5} = 8
\]

Thus, the solution is:

\[
? = 8
\]