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Which expression is equivalent to (111)4(11^1)^4?\newlineChoices:\newline(A) 11411^4\newline(B) 1115\frac{1}{11^5}\newline(C) 1114\frac{1}{11^4}\newline(D) 11511^5

Full solution

Q. Which expression is equivalent to (111)4(11^1)^4?\newlineChoices:\newline(A) 11411^4\newline(B) 1115\frac{1}{11^5}\newline(C) 1114\frac{1}{11^4}\newline(D) 11511^5
  1. Understand 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=amn(a^m)^n = a^{m*n}
  2. Apply Rule to Calculation: Apply the exponent rule to 11^1)^4\. We have \$11 raised to the power of 11, and this result is then raised to the power of 44. \(11^11)^44 = 1111^{(11*44)} = 1111^44\
  3. Choose Equivalent Expression: Choose the equivalent expression for \(11^11)^44\. According to the calculation in Step 22, \(11^11)^44\ is equivalent to (11\)^44\.

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