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

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Full solution

Q. If 2a=257 2^a = \sqrt[7]{2^5} , what is the value of a a ?
  1. Rewrite using exponents: First, rewrite the equation 2a=2572^a=\sqrt[7]{2^5} using exponents.\newline257=25/7\sqrt[7]{2^5} = 2^{5/7}
  2. Set exponents equal: Now, we have 2a=25/72^a = 2^{5/7}. Since the bases are the same, we can set the exponents equal to each other.\newlinea=57a = \frac{5}{7}

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