Answer:
1) Option A) is correct
The given rational exponent expression is not simplified correctly as a radical expression is
[tex]x^{\frac{7}{4}}=\sqrt[7]{x^4}[/tex]
2)Option A) is correct
That is [tex](729x^3y^{-18})^{\frac{1}{6}}=\frac{3\sqrt{x}}{y^3}[/tex]
Step-by-step explanation:
1) Given that [tex]x^{\frac{7}{4}}=(\sqrt{x^7})^\frac{1}{4}[/tex]
[tex]x^{\frac{7}{4}}=\sqrt[4]{x^7}[/tex] is the correct answer but in the given problem they gave the RHS as wrong.
Therefore the given rational exponent expression is not simplified correctly as a radical expression is
[tex]x^{\frac{7}{4}}=\sqrt[7]{x^4}[/tex]
2)Given that the rational exponent expression is [tex](729x^3y^{-18})^{\frac{1}{6}}[/tex]
To find it as a radical expression:
[tex](729x^3y^{-18})^{\frac{1}{6}}=(729)^{\frac{1}{6}}(x^3)^{\frac{1}{6}}((y^{-18})^{\frac{1}{6}})[/tex]
[tex]=3(x^{\frac{3}{6}})(y^{\frac{-18}{6}})[/tex]
[tex]=3(x^{\frac{1}{2}})(y^{-3})[/tex]
[tex]=\frac{3\sqrt{x}}{y^3}[/tex]
Therefore [tex](729x^3y^{-18})^{\frac{1}{6}}=\frac{3\sqrt{x}}{y^3}[/tex]
Therefore Option A) is correct
That is [tex](729x^3y^{-18})^{\frac{1}{6}}=\frac{3\sqrt{x}}{y^3}[/tex]
