A math puzzle for smart people with a brain for math! This challenge is for those who love to be challenged by mathematics and critical thinking problems. Let’s challenge your brain!

## Challenge:

If \(a = (5^{11})^{2}\) and \(b = 4^{11}\), how many digits long is ab?

**A-** 22

**B-** 23

**C-** 33

**D-** 44

**E-** 121

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The correct answer is B.

\(a = (511)^{2} = 5^{22}\) and \(b = 4^{11}\)

Change the base of number b from 4 to 2: \(b = 2^{22 }\)

Therefore, \(ab = 5^{22} × 2^{22 }= 10^{22}\)

Number \(10^{1}\) has 2 digits and number \(10^{2} (100)\) has 3 digits. Therefore, \(10^{22}\) has 23 digits.