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!
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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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![](https://www.effortlessmath.com/wp-content/uploads/2020/04/answer.png)
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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