Given the expression:
[tex]\frac{(x^{\frac{2}{3}})(y^2)^{}}{(x^{\frac{1}{2}})(y^2)}[/tex]
You can simplify it as follows:
1. By definition:
[tex]\frac{b}{b}=1[/tex]
Then:
[tex]=\frac{x^{\frac{2}{3}}^{}}{x^{\frac{1}{2}}}[/tex]
2. Apply the Quotient of Powers Property, which states that:
[tex]\frac{b^m}{b^n}=b^{m-n}[/tex]
Where "b" is the same base and "m" and "n" are exponents.
Then, you can set up:
[tex]=x^{\frac{2}{3}-\frac{1}{2}}[/tex]
You can use this formula to subtract the fractions:
[tex]\frac{a}{b}-\frac{c}{d}=\frac{ad-bc}{bd}[/tex]
Therefore, you get:
[tex]=x^{\frac{(2)(2)-(3)(1)}{(3)(2)}}[/tex][tex]=x^{\frac{4-3}{6}}[/tex][tex]=x^{\frac{1}{6}}[/tex]
Hence, the answer is: First option.
