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Which expression is equivalent to (32)1(3^2)^1?\newlineChoices:\newline(A) 133\frac{1}{3^3}\newline(B) 323^2\newline(C) 333^3\newline(D) 132\frac{1}{3^2}

Full solution

Q. Which expression is equivalent to (32)1(3^2)^1?\newlineChoices:\newline(A) 133\frac{1}{3^3}\newline(B) 323^2\newline(C) 333^3\newline(D) 132\frac{1}{3^2}
  1. Apply power rule: Apply the power of a power rule, which states that (am)n=a(mn)(a^m)^n = a^{(m*n)}.(32)1=3(21)(3^2)^1 = 3^{(2*1)}
  2. Calculate exponent: Calculate the exponent. 3(2×1)=323^{(2\times 1)} = 3^2
  3. Compare with choices: Compare the result with the given choices.\newline323^2 matches with choice (B).

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