What is the missing exponent in the following equation?

Question

e?e65 = e38
help me answer it

Answer 1

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

Using this property, we can rewrite the left side of the equation:

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

Now we can set the exponents equal to each other from both sides of the equation:

\[ ? + 65 = 38 \]

To find \( ? \), we can subtract 65 from both sides:

\[ ? = 38 - 65 \]

Calculating this gives:

\[ ? = -27 \]

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

Answer 2

no and more simpler

Answer 3

Sure! Let's solve the equation step by step in a simpler way.

You have:

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

We know that when we multiply exponents with the same base, we can add the exponents:

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

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

\[ ? + 65 = 38 \]

Now, to find \( ? \), subtract 65 from both sides:

\[ ? = 38 - 65 \]

Calculating that gives:

\[ ? = -27 \]

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

Answer 4

no -27 is wrong

Answer 5

Let's go through it again step by step to pinpoint any mistakes and present it as simply as possible.

You have the equation:

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

Using the property of exponents, \( e^a \cdot e^b = e^{a+b} \), we can rewrite the left side:

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

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

\[ ? + 65 = 38 \]

Now, to solve for \( ? \):

1. Subtract 65 from both sides: \[ ? = 38 - 65 \]

2. Performing the computation: \[ ? = -27 \]

This indicates that \( -27 \) is the correct calculation based on the equation provided.

If this still seems wrong, could you please clarify which part seems off or if there's additional context?