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Select all the expressions that are equivalent to 72×427^{-2} \times 4^{-2}.\newlineMulti-select Choices:\newline(A) 1282\frac{1}{28^{-2}}\newline(B) 28228^{-2}\newline(C) 1282\frac{1}{28^{2}}\newline(D) 28428^{4}

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Q. Select all the expressions that are equivalent to 72×427^{-2} \times 4^{-2}.\newlineMulti-select Choices:\newline(A) 1282\frac{1}{28^{-2}}\newline(B) 28228^{-2}\newline(C) 1282\frac{1}{28^{2}}\newline(D) 28428^{4}
  1. Simplify Expression: Step 11: Simplify the expression 72×427^{-2} \times 4^{-2}.\newlineCalculation: 727^{-2} means 1/721/7^2 and 424^{-2} means 1/421/4^2.\newlineSo, 72×42=(1/72)×(1/42)=1/(72×42)=1/49×16=1/7847^{-2} \times 4^{-2} = (1/7^2) \times (1/4^2) = 1/(7^2 \times 4^2) = 1/49 \times 16 = 1/784.
  2. Compare with Choices: Step 22: Compare the simplified expression with the choices.\newlineCalculation: 1/7841/784 needs to be compared with each choice.\newline(A) 1/282=1/(1/282)=282=7841/28^{-2} = 1/(1/28^2) = 28^2 = 784, not 1/7841/784.\newline(B) 282=1/282=1/78428^{-2} = 1/28^2 = 1/784, this matches.\newline(C) 1/282=1/7841/28^2 = 1/784, this also matches.\newline(D) 284=61465628^4 = 614656, not 1/7841/784.

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