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: \(c < a < b\)