What is the missing exponent in the following equation?

Question

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 \( 103 \).