Answer :
[tex]\mathbf{x}^{\mathbf{\frac{7}{6}}}[/tex]
1) Let's simplify the following product:
[tex]x^{\frac{1}{2}}\cdot x^{\frac{2}{3}}[/tex]Note that, we can simplify this using the exponent's properties.
2) So we can keep the base and add the exponents:
[tex]x^{\frac{1}{2}}\cdot x^{\frac{2}{3}}=x^{\frac{3+4}{6}}=x^{\frac{7}{6}}[/tex]Note that since the denominators were different, we had to resort to the LCM of 2 and 3 and simplify it to one fraction.
3) Hence, the answer is:
[tex]\mathbf{x}^{\mathbf{\frac{7}{6}}}[/tex]