Question

What is the missing exponent in the following equation?
e? /to the 65th power = e to the 38th power
(1 point)

Answer 1

To find the missing exponent in the equation \( e^? / e^{65} = e^{38} \), we can use the property of exponents that states \( \frac{e^a}{e^b} = e^{a-b} \).

Thus, we can rewrite the equation:

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

Setting this equal to \( e^{38} \):

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

Since the bases are the same, we can equate the exponents:

\[
? - 65 = 38
\]

Now, solving for \( ? \):

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

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