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Select all the expressions that are equivalent to (61)5(6^1)^5.\newlineMulti-select Choices:\newline(A) 656^5\newline(B) 165\frac{1}{6^{-5}}\newline(C) 166\frac{1}{6^6}\newline(D) 165\frac{1}{6^5}

Full solution

Q. Select all the expressions that are equivalent to (61)5(6^1)^5.\newlineMulti-select Choices:\newline(A) 656^5\newline(B) 165\frac{1}{6^{-5}}\newline(C) 166\frac{1}{6^6}\newline(D) 165\frac{1}{6^5}
  1. Simplify the base expression: Simplify the base expression (61)5(6^1)^5. Using the power of a power property, (am)n=a(mn)(a^m)^n = a^{(m*n)}, we get: (61)5=6(15)=65(6^1)^5 = 6^{(1*5)} = 6^5.
  2. Apply power of a power property: Compare the simplified expression 656^5 with each choice.\newline(A) 656^5 is clearly the same as 656^5.

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