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Select all the expressions that are equivalent to 12262\frac{12^2}{6^2}. \newlineMulti-select Choices:\newline(A) 2325\frac{2^{-3}}{2^{-5}}\newline(B) 22\newline(C) (22)1(2^{-2})^{-1}\newline(D) 222^2

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Q. Select all the expressions that are equivalent to 12262\frac{12^2}{6^2}. \newlineMulti-select Choices:\newline(A) 2325\frac{2^{-3}}{2^{-5}}\newline(B) 22\newline(C) (22)1(2^{-2})^{-1}\newline(D) 222^2
  1. Simplify and Calculate: First, simplify 12262 \frac{12^2}{6^2} . Calculate 122 12^2 and 62 6^2 :\newline122=144 12^2 = 144 ,\newline62=36 6^2 = 36 .\newlineNow, divide 144 144 by 36 36 :\newline14436=4 \frac{144}{36} = 4 .
  2. Evaluate Choices: Next, evaluate each choice to see if it equals 44:\newline(A) 2325 \frac{2^{-3}}{2^{-5}} simplifies to 2(3)(5)=22=4 2^{(-3)-(-5)} = 2^2 = 4 .
  3. Choice (A): (B) The value is simply 22, which does not equal 44.
  4. Choice (B): (C) (22)1 (2^{-2})^{-1} simplifies to 22=4 2^2 = 4 .
  5. Choice (C): (D) 22 2^2 is calculated directly as 44.

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