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Which expression is equivalent to (29)8(2^9)^8?\newlineChoices:\newline(A) 1272\frac{1}{2^{72}}\newline(B) 1217\frac{1}{2^{17}}\newline(C) 2722^{72}\newline(D) 2172^{17}

Full solution

Q. Which expression is equivalent to (29)8(2^9)^8?\newlineChoices:\newline(A) 1272\frac{1}{2^{72}}\newline(B) 1217\frac{1}{2^{17}}\newline(C) 2722^{72}\newline(D) 2172^{17}
  1. Simplify Power Rule: Simplify the expression using the power of a power rule, which states (am)n=amn(a^m)^n = a^{m*n}.\newlineCalculation: (29)8=298=272(2^9)^8 = 2^{9*8} = 2^{72}
  2. Calculate Exponent: Compare the simplified expression 2722^{72} with the given choices.\newline(A) 1272\frac{1}{2^{72}} is the reciprocal of 2722^{72}, not equivalent.\newline(B) 1217\frac{1}{2^{17}} is the reciprocal of 2172^{17}, not equivalent.\newline(C) 2722^{72} matches exactly.\newline(D) 2172^{17} is not equivalent as it represents a different power of 22.

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