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Select all the expressions that are equivalent to 26×292^6 \times 2^9.\newlineMulti-select Choices:\newline(A) (25)3(2^5)^3\newline(B) 1215615\frac{12^{15}}{6^{15}}\newline(C) 2542^{54}\newline(D) 2152^{15}

Full solution

Q. Select all the expressions that are equivalent to 26×292^6 \times 2^9.\newlineMulti-select Choices:\newline(A) (25)3(2^5)^3\newline(B) 1215615\frac{12^{15}}{6^{15}}\newline(C) 2542^{54}\newline(D) 2152^{15}
  1. Simplify Exponents: First, simplify 26×292^6 \times 2^9 using the properties of exponents.\newlineCalculation: 26×29=26+9=2152^6 \times 2^9 = 2^{6+9} = 2^{15}.
  2. Check Options: Next, check each option to see if it matches 2152^{15}.\newline(A) (25)3=25×3=215(2^5)^3 = 2^{5 \times 3} = 2^{15}.
  3. Option (A): (B) 1215/615=(12/6)15=21512^{15}/6^{15} = (12/6)^{15} = 2^{15}.
  4. Option (B): (C) 2542^{54} is clearly not equal to 2152^{15}, so this option is incorrect.
  5. Option (C): (D) 2152^{15} is exactly 2152^{15}, so this option is correct.

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