# Number Properties Puzzle – Challenge 7

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

### The Absolute Best Book** to ****challenge your Smart Student!**

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.

### More math articles

- 5th Grade Common Core Math Practice Test Questions
- Best Mobile Laptop Stands for Presentation in Schools
- 7th Grade K-PREP Math Worksheets: FREE & Printable
- Best Graphing Calculators for Precalculus
- Top 10 Tips You MUST Know to Retake the SSAT Math
- How to Prepare for the ALEKS Math Test?
- Who is the Greatest Mathematician of all time?
- 8th Grade Georgia Milestones Assessment System Math FREE Sample Practice Questions
- The Ultimate SAT Math Formula Cheat Sheet
- Full-Length ISEE Upper-Level Math Practice Test-Answers and Explanations

## What people say about "Number Properties Puzzle - Challenge 7"?

No one replied yet.