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Select all the expressions that are equivalent to (21)2(2^1)^2.\newlineMulti-select Choices:\newline(A) 232^3\newline(B) 122\frac{1}{2^2}\newline(C) 222^2\newline(D) 123\frac{1}{2^3}

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Q. Select all the expressions that are equivalent to (21)2(2^1)^2.\newlineMulti-select Choices:\newline(A) 232^3\newline(B) 122\frac{1}{2^2}\newline(C) 222^2\newline(D) 123\frac{1}{2^3}
  1. Simplify Expression: Simplify the expression (21)2(2^1)^2. Calculation: (21)2=22=4(2^1)^2 = 2^2 = 4.
  2. Compare with (A): Compare the simplified result with choice (A) 232^3. Calculation: 23=82^3 = 8. Since 848 \neq 4, (A) is not equivalent.
  3. Compare with (B): Compare the simplified result with choice (B) 122\frac{1}{2^2}. Calculation: 122=14\frac{1}{2^2} = \frac{1}{4}. Since 144\frac{1}{4} \neq 4, (B) is not equivalent.
  4. Compare with (C): Compare the simplified result with choice (C) 222^2. Calculation: 22=42^2 = 4. Since 4=44 = 4, (C) is equivalent.
  5. Compare with (D): Compare the simplified result with choice (D) 123\frac{1}{2^3}. Calculation: 123=18\frac{1}{2^3} = \frac{1}{8}. Since 184\frac{1}{8} \neq 4, (D) is not equivalent.

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