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Evaluate the left hand side to find the value of a in the equation in simplest form. (x^(2))^((1)/(3))=x^(a) Answer:

Evaluate the left hand side to find the value of a a in the equation in simplest form.\newline(x2)13=xa \left(x^{2}\right)^{\frac{1}{3}}=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)13=xa \left(x^{2}\right)^{\frac{1}{3}}=x^{a} \newlineAnswer:
  1. Identify Rule for Exponents: Identify the rule for exponents when raising a power to another power, which is to multiply the exponents. (x2)13(x^{2})^{\frac{1}{3}} simplifies to x2∗13x^{2*\frac{1}{3}}.
  2. Perform Exponent Multiplication: Perform the multiplication of the exponents. 2×(13)=23.2 \times \left(\frac{1}{3}\right) = \frac{2}{3}.
  3. Write Simplified Expression: Write the simplified expression with the new exponent. x2×(1/3)=x2/3.x^{2\times(1/3)} = x^{2/3}.
  4. Compare to Given Equation: Compare the simplified expression to the given equation. x23=xa.x^{\frac{2}{3}} = x^{a}.
  5. Determine Value of a: Determine the value of a by equating the exponents. a=23a = \frac{2}{3}.

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