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What is the value of A when we rewrite 8^(x) as A^(-(x)/(9)) ? Choose 1 answer: (A) A=8^(-9) (B) A=-(9)/(8) (C) A=8^((1)/(9)) (D) A=(-8)^((1)/(9))

What is the value of A A when we rewrite 8x 8^{x} as A−x9 A^{-\frac{x}{9}} ?\newlineChoose 11 answer:\newline(A) A=8−9 A=8^{-9} \newline(B) A=−98 A=-\frac{9}{8} \newline(C) A=819 A=8^{\frac{1}{9}} \newline(D) A=(−8)19 A=(-8)^{\frac{1}{9}}

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Q. What is the value of A A when we rewrite 8x 8^{x} as A−x9 A^{-\frac{x}{9}} ?\newlineChoose 11 answer:\newline(A) A=8−9 A=8^{-9} \newline(B) A=−98 A=-\frac{9}{8} \newline(C) A=819 A=8^{\frac{1}{9}} \newline(D) A=(−8)19 A=(-8)^{\frac{1}{9}}
  1. Expressing 88^x in the form of A^(-x/99): We need to express 8x 8^x in the form of A−x9 A^{-\frac{x}{9}} . To do this, we need to find a value for A A such that when raised to the power of −x9 -\frac{x}{9} , it is equivalent to 8x 8^x .
  2. Rewriting 88^x as (88^(11/99))^(99x): First, let's rewrite 8x 8^x as (819)9x (8^{\frac{1}{9}})^{9x} because 8x=(819)9x 8^x = (8^{\frac{1}{9}})^{9x} . This is because raising a number to a power and then raising it to another power is the same as multiplying the exponents.
  3. Taking the reciprocal of the base: Now, we want to match the form A−x9 A^{-\frac{x}{9}} . To do this, we need to take the reciprocal of the base inside the parentheses, which will change the sign of the exponent. So, (819)9x (8^{\frac{1}{9}})^{9x} can be written as (8−19)−9x (8^{-\frac{1}{9}})^{-9x} .
  4. Determining the value of A: We can now see that A A must be equal to 8−19 8^{-\frac{1}{9}} because (8−19)−9x (8^{-\frac{1}{9}})^{-9x} is in the form of A−x9 A^{-\frac{x}{9}} with A A being 8−19 8^{-\frac{1}{9}} .
  5. Correct answer: A = 88^(11/99): Therefore, the correct answer is A=819 A = 8^{\frac{1}{9}} , which corresponds to choice (C).

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