Question

1. simplify the expression: $(1^4 \times 2^2 + 3^3) - 2^5 \div 4$.\

a) -1\
b) 11\
c) 0\
d) 23

Explanation:

Step1: Calculate exponents

Calculate \(1^4 = 1\), \(2^2 = 4\), \(3^3 = 27\), \(2^5 = 32\).
The expression becomes \((1\times4 + 27)-32\div4\).

Step2: Perform multiplication and division

First, \(1\times4 = 4\), then \(32\div4 = 8\).
The expression is now \((4 + 27)-8\).

Step3: Perform addition and subtraction

\(4 + 27 = 31\), then \(31 - 8 = 23\). Wait, no, wait, let's recalculate: Wait, \(1^4\times2^2=1\times4 = 4\), \(3^3 = 27\), so inside the parentheses: \(4 + 27 = 31\). Then \(2^5\div4=32\div4 = 8\). Then \(31-8 = 23\)? Wait, but let's check again. Wait, \(1^4\) is 1, \(2^2\) is 4, so \(1\times4 = 4\). \(3^3\) is 27. So \(4 + 27 = 31\). \(2^5\) is 32, divided by 4 is 8. Then \(31 - 8 = 23\). So the answer is 23, which is option D. Wait, but let me check again. Wait, maybe I made a mistake. Wait, \(1^4\times2^2 = 1\times4 = 4\), \(3^3 = 27\), so \(4 + 27 = 31\). \(2^5 = 32\), \(32\div4 = 8\). Then \(31 - 8 = 23\). So the correct answer is D) 23. Wait, but let's check the options. Option D is 23. So that's correct.

Answer:

D) 23