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If 2a=257 2^a = \sqrt[7]{2^5} , what is the value of a a ?

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Q. If 2a=257 2^a = \sqrt[7]{2^5} , what is the value of a a ?
  1. Express with Same Base: To solve for aa, we need to express both sides of the equation with the same base and then equate the exponents.\newlineWe have 2a=(25)172^a = (2^5)^{\frac{1}{7}}.
  2. Equate Exponents: Since the bases are the same (base 22), we can equate the exponents. a=5×(17)a = 5 \times (\frac{1}{7})
  3. Perform Multiplication: Now, we perform the multiplication to find the value of aa.a=57a = \frac{5}{7}

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