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.
Reza is an experienced Math instructor and a test-prep expert who has been tutoring students since 2008. He has helped many students raise their standardized test scores--and attend the colleges of their dreams. He works with students individually and in group settings, he tutors both live and online Math courses and the Math portion of standardized tests. He provides an individualized custom learning plan and the personalized attention that makes a difference in how students view math.
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