The Solution:
The correct answer is:
[tex]\frac{y^{\frac{8}{3}}}{x^{\frac{1}{2}}}[/tex]
Explanation:
Given the expression below:
[tex]\frac{y^{\frac{4}{3}}x^{\frac{1}{2}}}{y^{}^{-\frac{4}{3}}x}[/tex]
We are required to simplify the above expression using the same notation.
[tex]\frac{y^{\frac{4}{3}}\times x^{\frac{1}{2}}}{y^{-\frac{4}{3}}\times x}=\frac{y^{\frac{4}{3}}}{y^{-\frac{4}{3}}}\times\frac{x^{\frac{1}{2}}}{x^1}[/tex]
This becomes
[tex]y^{\frac{4}{3}--\frac{4}{3}}\times x^{\frac{1}{2}-1}=y^{\frac{8}{3}}\times x^{-\frac{1}{2}}[/tex]
So we have,
[tex]\frac{y^{\frac{8}{3}}}{x^{\frac{1}{2}}}[/tex]
Therefore, the correct answer is
[tex]\frac{y^{\frac{8}{3}}}{x^{\frac{1}{2}}}[/tex]
