Here's a question I just made up. Difficulty level: 700ish If 2^m = 5 and 5^(1/n) = 3, then (3^n)/2^(-2m) = A) 1/25 B) 1/5 C) 5 D) 25 E) 125 Answer: E

Brent@GMATPrepNow wrote:Here's a question I just made up. Difficulty level: 700ish If 2^m = 5 and 5^(1/n) = 3, then (3^n)/2^(-2m) = A) 1/25 B) 1/5 C) 5 D) 25 E) 125 Answer: E If 2^m = 5 and 5^(1/n) = 3, we can substitute 2^m in place of 5 in the second equation to get 2^m^(1/n) = 3. Raise both sides to the n to get 2^m = 3^n. We're looking for (3^n)/2^(-2m), so substitute 2^m in place of 3^n, to get 2^m/2^(-2m) = 2^3m, or (2^m)^3. If 2^m = 5, then (2^m)^3 = 5^3 = 125. Answer is E

Brent@GMATPrepNow wrote:If 2^m = 5 and 5^(1/n) = 3, then (3^n)/2^(-2m) = A) 1/25 B) 1/5 C) 5 D) 25 E) 125 Another approach: Given: 2^m= 5 We need to determine the value of 2^(-2m) So, take 2^m= 5 and raise both sides to the power of -2 We get: (2^m)^(-2) = 5^(-2) Apply Power of a Power rule to get: 2^(-2m) = 5^(-2) Given: 5^(1/n) = 3 We need to determine the value of 3^n So, take 5^(1/n) = 3 and raise both sides to the power of n We get: [5^(1/n)]^n = 3^n Apply Power of a Power rule to get: 5^1 = 3^n So, (3^n)/2^(-2m) = (5^1)/[(5^(-2)] = 5^3 = 125 Answer: E

Brent@GMATPrepNow wrote:Here's a question I just made up. Difficulty level: 700ish If 2^m = 5 and 5^(1/n) = 3, then (3^n)/2^(-2m) = A) 1/25 B) 1/5 C) 5 D) 25 E) 125 An alternate approach is to BALLPARK. Since the answer choices are very spread out, we can approximate with integer values. Since 2² = 4, 2^m = 5 implies that m ≈ 2. Since √5 ≈ 2.24, 5^(1/n) = 3 implies that n ≈ 2. Thus: (3^n)/2^(-2m) ≈ (3²)/2¯� = (9)(16) = 144. Only E is viable. The correct answer is E.

Recognizing the relationship between what you want and what you're given is crucial here. We want 3� and 2�²�. We can get the first by raising 5⅟� to the n, and the second by raising 2� to the -2. Then we're set!