Quotient Rule of Exponents
What is the missing exponent in the following equation?
3
E?/e65 = e/38
To find the missing exponent in the equation, we can use the quotient rule of exponents:
a^m/a^n = a^(m-n)
In this case, we have:
3^E / 3^65 = 3^e / 3^38.
To find the missing exponent E, we can set up an equation using the quotient rule:
3^(E-65) = 3^(e-38).
Since the bases (3) are the same, the exponents must be equal. Therefore, we have:
E - 65 = e - 38.
To solve for E, we can rearrange the equation:
E = e - 38 + 65.
Simplifying further:
E = e + 27.
To find the missing exponent, we can use the quotient rule of exponents, which states that when dividing two exponential terms with the same base, we subtract the exponents.
In the given equation:
3^E / 3^65 = 3^e / 3^38
Using the quotient rule of exponents, we can equate the bases and subtract the exponents:
E - 65 = e - 38
Now, we can solve for the missing exponent E:
E = e - 38 + 65
Simplifying the expression further:
E = e + 27
Therefore, the missing exponent is E = e + 27.