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If 3a=353^a= \sqrt[5]{3}, what is the value of aa?

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Q. If 3a=353^a= \sqrt[5]{3}, what is the value of aa?
  1. Understand the Problem: Understand the problem.\newlineWe need to find the value of aa such that 3a3^a is equal to the fifth root of 33, which is written as 53^5\sqrt{3} or 3(1/5)3^{(1/5)}.
  2. Write as Exponent: Write the fifth root of 33 as an exponent.\newlineThe fifth root of 33 can be written as 3153^{\frac{1}{5}}.
  3. Set up Equation: Set up the equation.\newlineWe have 3a=3153^a = 3^{\frac{1}{5}}.
  4. Solve for aa: Solve for aa.\newlineSince the bases are the same, we can set the exponents equal to each other. Therefore, a=15a = \frac{1}{5}.

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