Question

What is the missing exponent in the following equation?%0D%0Ae?e65 = e38%0D%0A𝑒%0D%0A?%0D%0A𝑒%0D%0A65%0D%0A %0D%0A=%0D%0A %0D%0A𝑒%0D%0A38%0D%0A(1 poin

Answer 1

To solve for the missing exponent in the equation \( e^{?} \cdot e^{65} = e^{38} \), we can use the properties of exponents.

The left side of the equation can be combined since the bases (e) are the same:

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

Since the bases are the same, we can set the exponents equal to one another:

\[
? + 65 = 38
\]

To find the missing exponent (?), subtract 65 from both sides:

\[
? = 38 - 65
\]
\[
? = -27
\]

Thus, the missing exponent is \(-27\).