2^258 / 2^n = 512, find n.

Step-by-Step Solution

1. Apply the Quotient Rule of Exponents: The rule states that a^m / a^n = a^(m-n). So, 2^258 / 2^n = 2^(258-n).

2. Express 512 as a power of 2: We know that 2^9 = 512.

3. Equate the exponents: Now the equation is 2^(258-n) = 2^9. Since the bases are the same, their exponents must be equal: 258 - n = 9

4. Solve for n: n = 258 - 9 n = 249