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Which expression is equivalent to 27×262^7 \times 2^6?\newlineChoices:\newline(A) 2132^{13}\newline(B) 1242\frac{1}{2^{42}}\newline(C) 1213\frac{1}{2^{13}}\newline(D) 2422^{42}

Full solution

Q. Which expression is equivalent to 27×262^7 \times 2^6?\newlineChoices:\newline(A) 2132^{13}\newline(B) 1242\frac{1}{2^{42}}\newline(C) 1213\frac{1}{2^{13}}\newline(D) 2422^{42}
  1. Identify Base and Exponents: Identify the base and the exponents.\newlineIn 272^7 and 262^6, 22 is the base raised to the exponents 77 and 66 respectively.\newlineBase: 22\newlineExponents: 77, 66
  2. Rewrite Expression: Given expression: 27×262^7 \times 2^6\newlineRewrite this expression as a single power of 22.\newlineWhen we multiply powers with the same base, we add the exponents.\newline27×262^7 \times 2^6\newline=27+6= 2^{7+6}\newline=213= 2^{13}
  3. Choose Equivalent Expression: Choose the equivalent expression for 27×262^7 \times 2^6.\newline27×26=2132^7 \times 2^6 = 2^{13}\newlineThe equivalent expression is 2132^{13}, which corresponds to choice (A).