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Question 1 / 3
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1
What is the value of (1/512)^(1/9)?
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Solution: Step 1: Express 512 as a power of 2, since 512 = 2^9. Step 2: Rewrite (1/512)^(1/9) as (1/(2^9))^(1/9). Step 3: Apply exponent rule: (a^m)^n = a^(m*n). Step 4: This gives (2^(-9))^(1/9) = 2^(-9 * 1/9) = 2^(-1). Step 5: Simplify 2^(-1) to 1/2.
2
Which of the given expressions yields the largest value?
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Solution: Step 1: Evaluate each expression Step 2: Option A: 16^(2/3) = (2^4)^(2/3) = 2^(8/3) = 2^2 * 2^(2/3) = 4 * 2^(2/3) ≈ 4 * 1.5874 ≈ 6.35 Step 3: Option B: 125^(4/3) = (5^3)^(4/3) = 5^4 = 625 Step 4: Option C: 27^(2/3) = (3^3)^(2/3) = 3^2 = 9 Step 5: Option D: 1024^(4/5) = (2^10)^(4/5) = 2^8 = 256 Step 6: Comparing the calculated values: 6.35, 625, 9, 256 Step 7: The largest value is 625, from option B: 125^(4/3)
3
Solve the expression: (1/343)^(-2/3) / (1/49)^(3/2)
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Solution: Step 1: Rewrite the terms using exponent rules (1/343)^(-2/3) = (7^(-3))^(-2/3) = 7^2 = 49 (1/49)^(3/2) = (7^(-2))^(3/2) = 7^(-3) = 1/343 Step 2: Divide the two expressions 49 / (1/343) = 49 * 343 = 16807 Therefore, the correct answer is 16807.
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