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Select the equivalent expression 6×6×6×6×66\times 6\times 6\times 6\times 6\newline(A) (62)3(6^2)^3\newline(B) 25352^5 \cdot 3^5\newline(C) 6661\frac{6^6}{6^1}\newline(D) 32233^2 \cdot 2^3

Full solution

Q. Select the equivalent expression 6×6×6×6×66\times 6\times 6\times 6\times 6\newline(A) (62)3(6^2)^3\newline(B) 25352^5 \cdot 3^5\newline(C) 6661\frac{6^6}{6^1}\newline(D) 32233^2 \cdot 2^3
  1. Evaluate Options: We need to find an expression that is equivalent to multiplying 66 by itself 55 times, which is written as 656^5. Let's evaluate each option to see which one is equivalent to 656^5.
  2. Option (A): Option (A) is (62)3(6^2)^3. Using the power of a power rule, which states that (am)n=amn(a^m)^n = a^{m*n}, we calculate (62)3(6^2)^3 as 623=666^{2*3} = 6^6. This is not equal to 656^5.
  3. Option (B): Option (B) is 25×352^5 \times 3^5. Using the rule that (ab)n=an×bn(ab)^n = a^n \times b^n, we can rewrite 656^5 as (2×3)5(2\times3)^5, which is equal to 25×352^5 \times 3^5. This option is equivalent to 656^5.
  4. Option (C): Option (C) is 66/616^6/6^1. Using the quotient of powers rule, which states that am/an=a(mn)a^m / a^n = a^{(m-n)}, we calculate 66/616^6/6^1 as 6(61)=656^{(6-1)} = 6^5. This option is also equivalent to 656^5.
  5. Option (D): Option (D) is 32×233^2 \times 2^3. This option is not equivalent to 656^5 because 32×23=9×8=723^2 \times 2^3 = 9 \times 8 = 72, which is not the same as 66 multiplied by itself 55 times.

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