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What is the value of 
A when we rewrite 
((5)/(6))^(x) as 
A^(-8x) ?
Choose 1 answer:
(A)

A=((5)/(6))^((1)/(8))
(B)

A=((5)/(6))^(-(1)/(8))
(C) 
A=-8*(5)/(6)
(D) 
A=(1)/(8)

What is the value of A A when we rewrite (56)x \left(\frac{5}{6}\right)^{x} as A8x A^{-8 x} ?\newlineChoose 11 answer:\newline(A) A=(56)18A=\left(\frac{5}{6}\right)^{\frac{1}{8}} \newline(B) A=(56)18A=\left(\frac{5}{6}\right)^{-\frac{1}{8}}\newline(C) A=856 A=-8 \cdot \frac{5}{6} \newline(D) A=18 A=\frac{1}{8}

Full solution

Q. What is the value of A A when we rewrite (56)x \left(\frac{5}{6}\right)^{x} as A8x A^{-8 x} ?\newlineChoose 11 answer:\newline(A) A=(56)18A=\left(\frac{5}{6}\right)^{\frac{1}{8}} \newline(B) A=(56)18A=\left(\frac{5}{6}\right)^{-\frac{1}{8}}\newline(C) A=856 A=-8 \cdot \frac{5}{6} \newline(D) A=18 A=\frac{1}{8}
  1. Identify Base AA: To rewrite (56)x\left(\frac{5}{6}\right)^x as A8xA^{-8x}, we need to find a base AA such that raising AA to the power of 8x-8x gives us the same expression as (56)x\left(\frac{5}{6}\right)^x.
  2. Equating Expressions: We can start by equating the two expressions: (56)x=A8x\left(\frac{5}{6}\right)^x = A^{-8x}
  3. Find Value of A: To find AA, we need to express (56)x\left(\frac{5}{6}\right)^x in a form that makes the exponent 8x-8x. We can do this by raising (56)\left(\frac{5}{6}\right) to the power of 18\frac{1}{8} and then inverting the exponent to make it negative:\newlineA=(56)(18)A = \left(\frac{5}{6}\right)^{\left(\frac{1}{8}\right)}
  4. Rewrite Using A: Now, we can rewrite the original expression using the value of A we found: (56)x=((56)18)8x\left(\frac{5}{6}\right)^x = \left( \left(\frac{5}{6}\right)^{\frac{1}{8}} \right)^{-8x}
  5. Correct Answer: This means that the correct answer is (A) A=(56)18A=\left(\frac{5}{6}\right)^{\frac{1}{8}}, since this is the value of AA that allows us to rewrite (56)x\left(\frac{5}{6}\right)^x as A8xA^{-8x}.

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