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If 7a=7387^a=\sqrt[8]{7^3}, what is the value of a?a?

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Full solution

Q. If 7a=7387^a=\sqrt[8]{7^3}, what is the value of a?a?
  1. Express with same base: We need to express both sides of the equation with the same base and exponent format. 7a=(73)187^a = (7^3)^{\frac{1}{8}}
  2. Simplify right side: Now, let's simplify the right side of the equation by applying the exponent rule (xm)n=x(m∗n)(x^m)^n = x^{(m*n)}.\newline7a=7387^a = 7^{\frac{3}{8}}
  3. Set exponents equal: Since the bases are the same, we can set the exponents equal to each other. a=38a = \frac{3}{8}

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