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Evaluate the left hand side to find the value of a in the equation in simplest form. x^(3)x^((1)/(5))=x^(a) Answer:

Evaluate the left hand side to find the value of a a in the equation in simplest form.\newlinex3x15=xa x^{3} x^{\frac{1}{5}}=x^{a} \newlineAnswer:

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Q. Evaluate the left hand side to find the value of a a in the equation in simplest form.\newlinex3x15=xa x^{3} x^{\frac{1}{5}}=x^{a} \newlineAnswer:
  1. Use Exponent Property: To find the value of aa, we need to use the property of exponents that states when you multiply powers with the same base, you add the exponents.\newlineCalculation: x3×x15=x3+15x^{3} \times x^{\frac{1}{5}} = x^{3 + \frac{1}{5}}
  2. Convert to Improper Fraction: Convert the mixed number to an improper fraction to add the exponents easily.\newlineCalculation: 3+15=155+15=1653 + \frac{1}{5} = \frac{15}{5} + \frac{1}{5} = \frac{16}{5}
  3. Equate to Find a: Now that we have the sum of the exponents, we can equate it to aa.\newlineCalculation: x3×x15=x165=xax^{3} \times x^{\frac{1}{5}} = x^{\frac{16}{5}} = x^{a}\newlineTherefore, a=165a = \frac{16}{5}

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