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Which expression is equivalent to (27)6(2^7)^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)6(2^7)^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. Understand Exponent Rule: Understand the exponent rule for powers raised to powers.\newlineWhen we have a power raised to another power, we multiply the exponents.\newline(am)n=a(mn)(a^m)^n = a^{(m*n)}
  2. Apply Rule to Calculation: Apply the exponent rule to (27)6(2^7)^6. We multiply the exponents 77 and 66. (27)6=2(76)=242(2^7)^6 = 2^{(7*6)} = 2^{42}
  3. Choose Equivalent Expression: Choose the equivalent expression for (27)6(2^7)^6. From the calculation in Step 22, we have determined that (27)6(2^7)^6 is equivalent to 2422^{42}.

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