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What is the value of AA when we rewrite (56)x\left(\dfrac{5}{6}\right)^{x} as [A8x][A^{-8x}] ?\newlineA) \left(\dfrac{55}{66}\right)^{8-8}\newlineB) \left(\dfrac{66}{55}\right)^{88}\newlineC) \left(\dfrac{55}{66}\right)^{88}\newlineD) \left(\dfrac{66}{55}\right)^{8-8}

Full solution

Q. What is the value of AA when we rewrite (56)x\left(\dfrac{5}{6}\right)^{x} as [A8x][A^{-8x}] ?\newlineA) \left(\dfrac{55}{66}\right)^{8-8}\newlineB) \left(\dfrac{66}{55}\right)^{88}\newlineC) \left(\dfrac{55}{66}\right)^{88}\newlineD) \left(\dfrac{66}{55}\right)^{8-8}
  1. Rewrite in desired form: First, we need to rewrite (56)x\left(\dfrac 56\right)^{x} in the form A8xA^{-8x}.
  2. Equating exponents: We know that (56)x=A8x\left(\dfrac 56\right)^{x} = A^{-8x}.
  3. Solving for A: To find AA, we need to equate the exponents. So, (56)=A8\left(\dfrac 56\right) = A^{-8}.
  4. Finding A value: Take the 88th root of both sides to solve for AA. So, A=(56)1/8A = \left(\dfrac 56\right)^{-1/8}.
  5. Simplify the expression: Simplify the expression. A=(65)1/8A = \left(\dfrac 65\right)^{1/8}.