What is the missing exponent in the following equation?

Question

e?/e65 = e38
(1 point)

Answer 1

To solve the equation \( \frac{e^?}{e^{65}} = e^{38} \), we can use the properties of exponents.

First, we can simplify the left side of the equation:

\[ \frac{e^?}{e^{65}} = e^{? - 65} \]

So we can rewrite the equation as:

\[ e^{? - 65} = e^{38} \]

Since the bases are the same (both are \( e \)), we can set the exponents equal to each other:

\[ ? - 65 = 38 \]

Now, we can solve for \( ? \):

\[ ? = 38 + 65 \] \[ ? = 103 \]

Thus, the missing exponent is \( \boxed{103} \).