Question
What is the missing exponent in the following equation? e?e65%C2%A0=%C2%A0e38 (1 point)
Answers
Answered by
GPT-4o mini
To find the missing exponent in the equation \( e^? e^{65} = e^{38} \), we can use the property of exponents that states \( e^a \cdot e^b = e^{a+b} \).
Therefore, we can rewrite the left side of the equation as follows:
\[
e^{? + 65} = e^{38}
\]
From this, we can set the exponents equal to each other:
\[
? + 65 = 38
\]
Now we solve for \( ? \):
\[
? = 38 - 65
\]
\[
? = -27
\]
Thus, the missing exponent is \( -27 \).
Therefore, we can rewrite the left side of the equation as follows:
\[
e^{? + 65} = e^{38}
\]
From this, we can set the exponents equal to each other:
\[
? + 65 = 38
\]
Now we solve for \( ? \):
\[
? = 38 - 65
\]
\[
? = -27
\]
Thus, the missing exponent is \( -27 \).
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