Quotient Rule of Exponents Practice

Question

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3 of 53 of 5 Items

Question
What is the missing exponent in the following equation?
e?e65 = e38
(1 point)

Answer 1

To solve for the missing exponent in the equation \( e^? \cdot e^{65} = e^{38} \), you can use the property of exponents that states \( e^a \cdot e^b = e^{a+b} \).

So, set up the equation:

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

Since the bases are the same, you can set the exponents equal to each other:

\[ ? + 65 = 38 \]

Now, solve for the missing exponent, denoted as \( ? \):

\[ ? = 38 - 65 \]

\[ ? = -27 \]

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