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Which of the following is equivalent to (2^(x))^(3) ? Choose 1 answer: (A) 6^(x) (B) 6^(x^(3)) (C) 8^(x) (D) 8^(3x)

Which of the following is equivalent to (2x)3 \left(2^{x}\right)^{3} ?\newlineChoose 11 answer:\newline(A) 6x 6^{x} \newline(B) 6x3 6^{x^{3}} \newline(C) 8x 8^{x} \newline(D) 83x 8^{3 x}

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Full solution

Q. Which of the following is equivalent to (2x)3 \left(2^{x}\right)^{3} ?\newlineChoose 11 answer:\newline(A) 6x 6^{x} \newline(B) 6x3 6^{x^{3}} \newline(C) 8x 8^{x} \newline(D) 83x 8^{3 x}
  1. Simplify expression using laws of exponents: We need to simplify the expression (2x)3(2^{x})^{3} using the laws of exponents.\newlineAccording to the laws of exponents, (am)n=am∗n(a^{m})^{n} = a^{m*n}.\newlineSo, (2x)3=2x∗3(2^{x})^{3} = 2^{x*3}.
  2. Perform multiplication inside the exponent: Now we perform the multiplication inside the exponent.\newlinex×3=3xx \times 3 = 3x.\newlineSo, 2(x×3)=23x2^{(x \times 3)} = 2^{3x}.
  3. Compare simplified expression with given choices: We compare the simplified expression with the given choices.\newline23x2^{3x} matches with choice (D) 83x8^{3x}.\newlineHowever, we need to verify if 23x2^{3x} is indeed equal to 83x8^{3x}.\newlineWe know that 88 is 22 raised to the power of 33, i.e., 8=238 = 2^3.\newlineSo, 23x2^{3x} is not equal to 83x8^{3x} because 83x8^{3x} would imply 83x8^{3x}11, which is not the same as 23x2^{3x}.

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