Question 194964
*[Tex \LARGE \left(3^{\frac{1}{2}}8^{\frac{1}{3}}\right)^{2}] ... Start with the given expression.




*[Tex \LARGE 3^{2\ast\frac{1}{2}}8^{2\ast\frac{1}{3}}] ... Multiply the outer exponent by EVERY exponent in the parenthesis.



*[Tex \LARGE 3^{\frac{2}{2}}8^{\frac{2}{3}}] ... Multiply



*[Tex \LARGE 3^{1}8^{\frac{2}{3}}] ... Reduce



*[Tex \LARGE 3\ast8^{\frac{2}{3}}] ... Simplify



*[Tex \LARGE 3\ast\left(\sqrt[3]{8}\right)^2] ... Convert to radical notation.



*[Tex \LARGE 3\ast\left(2\right)^2] ... Take the cube root of 8 to get 2



*[Tex \LARGE 3\ast4] ... Square 2 to get 4



*[Tex \LARGE 12] ... Multiply




So *[Tex \LARGE \left(3^{\frac{1}{2}}8^{\frac{1}{3}}\right)^{2}=12]