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Select all the expressions that are equivalent to 6222\frac{6^2}{2^2}. \newlineMulti-select Choices:\newline(A) 303^0\newline(B) 13−2\frac{1}{3^{-2}}\newline(C) 323^2\newline(D) 132\frac{1}{3^2}

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Full solution

Q. Select all the expressions that are equivalent to 6222\frac{6^2}{2^2}. \newlineMulti-select Choices:\newline(A) 303^0\newline(B) 13−2\frac{1}{3^{-2}}\newline(C) 323^2\newline(D) 132\frac{1}{3^2}
  1. Calculate Result: Calculate 6222 \frac{6^2}{2^2} .\newline62=36 6^2 = 36 and 22=4 2^2 = 4 , so 364=9 \frac{36}{4} = 9 .
  2. Compare with Choices: Compare the result with each choice.\newline(A) 30=1 3^0 = 1 - not equal to 99.
  3. Check Choice (B): Check choice (B) 13−2 \frac{1}{3^{-2}} .\newline3−2=19 3^{-2} = \frac{1}{9} , so 119=9 \frac{1}{\frac{1}{9}} = 9 - this matches.
  4. Check Choice (C): Check choice (C) 32 3^2 .\newline32=9 3^2 = 9 - this matches too.
  5. Check Choice (D): Check choice (D) 132 \frac{1}{3^2} .\newline32=9 3^2 = 9 , so 19 \frac{1}{9} - not equal to 99.

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