Question

What is the missing exponent in the following equation? e^?divide by e^65=e^38

Answer 1

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

According to the laws of exponents, we know that:

\[
\frac{e^a}{e^b} = e^{a-b}
\]

Applying this to our equation:

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

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

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

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

\[
? - 65 = 38
\]

Now, solve for \( ? \):

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

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