10 Views
Question : What is the simplified value of $(2+1)(2^{2}+1)(2^{4}+1)(2^{8}+1)$?
Option 1: $2^{8}-1$
Option 2: $2^{16}-1$
Option 3: $2^{32}-1$
Option 4: $2^{64}-1$
Answer (1)
Correct Answer: $2^{16}-1$
Solution :
Given: $(2+1)(2^{2}+1)(2^{4}+1)(2^{8}+1)$
Multiplying (2 – 1) = 1 in the equation, we get:
$(2-1)(2+1)(2^{2}+1)(2^{4}+1)(2^{8}+1)$
= $(2^2-1)(2^{2}+1)(2^{4}+1)(2^{8}+1)$
= $(2^4-1)(2^{4}+1)(2^{8}+1)$
= $(2^8-1)(2^{8}+1)$
= $(2^{16}-1)$
Hence, the correct answer is $(2^{16}-1)$.
Know More About
Related Questions
TOEFL ® Registrations 2024
Apply
Accepted by more than 11,000 universities in over 150 countries worldwide
Upcoming Exams
Admit Card Date:
8 Apr, 2025
- 19 Apr, 2025
Application Date:
7 Apr, 2025
- 3 May, 2025
Mains Exam
Result Date:
1 Apr, 2025
- 30 Apr, 2025
Result Date:
1 Apr, 2025
- 30 Apr, 2025
Application Date:
28 Mar, 2025
- 29 Apr, 2025
Trending Articles around SSC CPO
REET 2025: Level 1 & Level 2 Scorecard (Soon), Cutoff,
55 minutes ago