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What is the value of A when we rewrite ((7)/(3))^(x) as A^(2x) ? Choose 1 answer: (A) A=(1)/(2) (B) A=((7)/(3))^((1)/(2)) (c) A=((7)/(3))^(-2) (D) A=(3)/(7)

What is the value of A A when we rewrite (73)x \left(\frac{7}{3}\right)^{x} as A2x A^{2 x} ?\newlineChoose 11 answer:\newline(A) A=12 A=\frac{1}{2} \newline(B) A=(73)12 A=\left(\frac{7}{3}\right)^{\frac{1}{2}} \newline(C) A=(73)−2 A=\left(\frac{7}{3}\right)^{-2} \newline(D) A=37 A=\frac{3}{7}

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Q. What is the value of A A when we rewrite (73)x \left(\frac{7}{3}\right)^{x} as A2x A^{2 x} ?\newlineChoose 11 answer:\newline(A) A=12 A=\frac{1}{2} \newline(B) A=(73)12 A=\left(\frac{7}{3}\right)^{\frac{1}{2}} \newline(C) A=(73)−2 A=\left(\frac{7}{3}\right)^{-2} \newline(D) A=37 A=\frac{3}{7}
  1. Given expression: We are given the expression (73)x\left(\frac{7}{3}\right)^{x} and we want to rewrite it in the form A2xA^{2x}. To do this, we need to find a base AA such that A2xA^{2x} is equivalent to (73)x\left(\frac{7}{3}\right)^{x}.
  2. Equating the expressions: To find AA, we need to equate the two expressions:\newline(73)x=A2x\left(\frac{7}{3}\right)^{x} = A^{2x}\newlineSince the exponents must be the same for the bases to be equal, we can rewrite the right side to have the same exponent as the left side by taking the square root of AA:\newline(73)x=(A2)x\left(\frac{7}{3}\right)^{x} = (A^2)^{x}
  3. Finding A: Now we can equate the bases:\newline(73)=A2(\frac{7}{3}) = A^2\newlineTo find A, we take the square root of both sides:\newlineA=73A = \sqrt{\frac{7}{3}}
  4. Simplifying the square root: Simplifying the square root of the fraction, we get:\newlineA=(73)12A = \left(\frac{7}{3}\right)^{\frac{1}{2}}\newlineThis matches one of the given answer choices.

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