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What is the value of A when we rewrite 4^(31 x) as A^(x) ? Choose 1 answer: (A) A=(4)/(31) (B) A=4^(31) (c) A=4*31 (D) A=31^(4)

What is the value of A A when we rewrite 431x 4^{31 x} as Ax A^{x} ?\newlineChoose 11 answer:\newline(A) A=431 A=\frac{4}{31} \newline(B) A=431 A=4^{31} \newline(C) A=4⋅31 A=4 \cdot 31 \newline(D) A=314 A=31^{4}

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Full solution

Q. What is the value of A A when we rewrite 431x 4^{31 x} as Ax A^{x} ?\newlineChoose 11 answer:\newline(A) A=431 A=\frac{4}{31} \newline(B) A=431 A=4^{31} \newline(C) A=4⋅31 A=4 \cdot 31 \newline(D) A=314 A=31^{4}
  1. Problem Understanding: Understand the problem.\newlineWe need to express 431x4^{31x} in the form of AxA^{x}, where AA is a constant that does not depend on xx.
  2. Expression Rewrite: Rewrite the expression.\newlineSince we want to express 431x4^{31x} as AxA^{x}, we need to find a value for AA such that Ax=431xA^{x} = 4^{31x}.
  3. Base and Exponent Identification: Identify the base and the exponent.\newlineIn the expression 431x4^{31x}, the base is 44 and the exponent is 31x31x. We want to keep the exponent as xx in the new expression AxA^{x}.
  4. Finding the Value of A: Find the value of A.\newlineTo keep the exponent as xx, AA must be equal to 44 raised to the power of 3131, because (431)x=431x(4^{31})^x = 4^{31x}.
  5. Choosing the Correct Answer: Choose the correct answer.\newlineFrom the options given, the correct answer is (B) A=431A = 4^{31}.

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