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Rewrite the expression in the form xnx^{n}. \newlineWrite the exponent as an integer, fraction, or an exact decimal (not a mixed number).\newlinex2x234=□\sqrt[4]{\frac{x^{2}}{x^{\frac{2}{3}}}}=\square

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Full solution

Q. Rewrite the expression in the form xnx^{n}. \newlineWrite the exponent as an integer, fraction, or an exact decimal (not a mixed number).\newlinex2x234=□\sqrt[4]{\frac{x^{2}}{x^{\frac{2}{3}}}}=\square
  1. Apply Exponent Property: Apply the property of exponents that states (xa)/(xb)=xa−b(x^{a})/(x^{b}) = x^{a-b} to the expression inside the fourth root.(x2x23)4=x2−234\sqrt[4]{\left(\frac{x^{2}}{x^{\frac{2}{3}}}\right)} = \sqrt[4]{x^{2 - \frac{2}{3}}}
  2. Subtract Exponents: Subtract the exponents: 2−(23)=(63)−(23)=432 - \left(\frac{2}{3}\right) = \left(\frac{6}{3}\right) - \left(\frac{2}{3}\right) = \frac{4}{3}. x2−(23)4=x434\sqrt[4]{x^{2 - \left(\frac{2}{3}\right)}} = \sqrt[4]{x^{\frac{4}{3}}}
  3. Apply Root Property: Apply the property of exponents that states xmn=xmn\sqrt[n]{x^{m}} = x^{\frac{m}{n}} to the expression.x434=x(43)/4\sqrt[4]{x^{\frac{4}{3}}} = x^{\left(\frac{4}{3}\right)/4}
  4. Simplify Exponent: Simplify the exponent by dividing 43\frac{4}{3} by 44, which is the same as multiplying 43\frac{4}{3} by 14\frac{1}{4}. \newlinex(43)/4=x(43)⋅(14)=x13x^{\left(\frac{4}{3}\right)/4} = x^{\left(\frac{4}{3}\right)\cdot\left(\frac{1}{4}\right)} = x^{\frac{1}{3}}

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