What is the missing exponent in the following equation? (e ^ 7)/(e ^ 65) = e ^ 38 (1 point)
The missing exponent in the equation is -28.
To find the missing exponent in the equation, we need to set up an equation and solve for the missing exponent.
Given equation: (e ^ 7) / (e ^ 65) = e ^ 38
When dividing exponential expressions with the same base, you subtract the exponents:
(e ^ (7 - 65)) = e ^ 38
Simplifying the exponent on the left side:
e ^ (-58) = e ^ 38
To make the bases equal, we set the exponents equal to each other:
-58 = 38
Since -58 does not equal 38, there is no missing exponent that would make the equation true.
To find the missing exponent in the equation (e^7)/(e^65) = e^38, we can apply the rules of exponents.
The equation (e^7)/(e^65) = e^38 involves the same base, which is e.
When dividing two exponential expressions with the same base, you subtract the exponents. So, we can rewrite the equation as e^(7-65) = e^38.
Simplifying further, we get e^(-58) = e^38.
Now, to find the missing exponent, we equate the exponents on both sides of the equation: -58 = 38.
However, -58 is not equal to 38. Therefore, there is no value for the missing exponent that would make this equation true.
Hence, the missing exponent in the equation (e^7)/(e^65) = e^38 is not possible; it cannot be determined.