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What is the value of A when we rewrite 6^(x) as A^((x)/(4)) ? Choose 1 answer: (A) A=4^((1)/(6)) (B) A=6^((1)/(4)) (C) A=(6)/(4) (D) A=6^(4)

What is the value of A A when we rewrite 6x 6^{x} as Ax4 A^{\frac{x}{4}} ?\newlineChoose 11 answer:\newline(A) A=416 A=4^{\frac{1}{6}} \newline(B) A=614 A=6^{\frac{1}{4}} \newline(C) A=64 A=\frac{6}{4} \newline(D) A=64 A=6^{4}

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Full solution

Q. What is the value of A A when we rewrite 6x 6^{x} as Ax4 A^{\frac{x}{4}} ?\newlineChoose 11 answer:\newline(A) A=416 A=4^{\frac{1}{6}} \newline(B) A=614 A=6^{\frac{1}{4}} \newline(C) A=64 A=\frac{6}{4} \newline(D) A=64 A=6^{4}
  1. Find Base A: To rewrite 6x6^{x} as A(x4)A^{\left(\frac{x}{4}\right)}, we need to find a base AA such that raising AA to the power of (x4)\left(\frac{x}{4}\right) will give us 6x6^{x}. This means that A4A^{4} must equal 66.
  2. Algebraic Expression: We can express this relationship algebraically as A4=6A^{4} = 6. To find AA, we take the fourth root of both sides of the equation.
  3. Take Fourth Root: Taking the fourth root of both sides gives us A=(6)14A = (6)^{\frac{1}{4}}.
  4. Final Answer: Therefore, the correct answer is (B) A=6(14)A=6^{(\frac{1}{4})}.

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