Number Properties Puzzle – Challenge 10
This is a great math challenge related to Number Properties for those who love critical thinking challenges. To solve this problem, you need to use your knowledge of exponents. Let's challenge your brain!
Challenge:
If \(a=2^{6000}, b=3^{4000}\) and \(c=7^{2000}\), which of the following is true?
A- \(a < b < c\)
B- \(c < b < a\)
C- \(a < c < b\)
D- \(c < a < b\)
E- \(b < a < c\)
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The correct answer is D.
\(a=2^{6000}, b=3^{4000}\) and \(c=7^{2000}\)
Find the \(2000^{th}\) rout of each number:
\(\sqrt[2000]{a}= \sqrt[2000]{2^{6000}} = 2^{\frac{6000}{2000}} = 2^3 = 8\)
\(\sqrt[2000]{b} =\sqrt[2000]{3^{4000}} = 3^{\frac{4000}{2000}} = 3^2 = 9\)
\(\sqrt[2000]{c} = \sqrt[2000]{7^{2000}} = 7^{\frac{2000}{2000}} = 7^1 = 7\)
Therefore: \(c < a < b\)
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