2^258 / 2^n = 512, find n.
2024
2^258 / 2^n = 512, find n.
Answer: D. 249 — Step-by-Step SolutionApply the Quotient Rule of Exponents: The rule states that a^m / a^n = a^(m-n). So, 2^258 / 2^n = 2^(258-n). Express 512 as a power of 2:…
- A.
248
- B.
250
- C.
251
- D.
249
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Correct answer: D
Step-by-Step Solution
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).
Express 512 as a power of 2: We know that 2^9 = 512.
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
Solve for n: n = 258 - 9 n = 249
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