Question

What is the missing exponent in the following equation?
e superscript ? over e superscript 65 = e superscript 38
(1 point)

Answer 1

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

1. Recall that \( \frac{e^a}{e^b} = e^{a-b} \).
2. Apply this property to the left-hand side of the equation:

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

3. Now we have:

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

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

\[
?-65 = 38
\]

5. To find the missing exponent (denoted as \( ? \)), add 65 to both sides:

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

Thus, the missing exponent is \( 103 \).