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Evaluate the left hand side to find the value of a in the equation in simplest form. (x^(2))^((1)/(6))=x^(a) Answer:

Evaluate the left hand side to find the value of a a in the equation in simplest form.\newline(x2)16=xa \left(x^{2}\right)^{\frac{1}{6}}=x^{a} \newlineAnswer:

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Full solution

Q. Evaluate the left hand side to find the value of a a in the equation in simplest form.\newline(x2)16=xa \left(x^{2}\right)^{\frac{1}{6}}=x^{a} \newlineAnswer:
  1. Apply power rule: Apply the power rule for exponents, which states that x^m)^n = x^{m*n}\, to the left hand side of the equation.\(x^{\(2\)})^{\frac{\(1\)}{\(6\)}} = x^{\(2\)*\frac{\(1\)}{\(6\)}}\
  2. Simplify exponents: Multiply the exponents to simplify the expression. \(2 \times \left(\frac{1}{6}\right) = \frac{2}{6}
  3. Reduce fraction: Reduce the fraction 26\frac{2}{6} to its simplest form.\newline26=13\frac{2}{6} = \frac{1}{3}
  4. Write simplified expression: Write the simplified expression for the left hand side of the equation. x26=x13x^{\frac{2}{6}} = x^{\frac{1}{3}}
  5. Equate exponents: Since the bases are the same and the equation is of the form xm=xnx^m = x^n, we can equate the exponents.\newline26=a\frac{2}{6} = a
  6. Substitute fraction: Substitute the simplified fraction for aa.a=13a = \frac{1}{3}

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