Question

Quotient Rule of Exponents
What is the missing exponent in the following equation?
3
E?/e65 = e/38

Answer 1

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.