Question

NEED HELP ASAP 70 POINTS

Answer 1

Answer:

1) Option A) is correct

The given rational exponent expression is not simplified correctly as a radical expression is

$x^{\frac{7}{4}}=\sqrt[7]{x^4}$

2)Option A) is correct

That is $(729x^3y^{-18})^{\frac{1}{6}}=\frac{3\sqrt{x}}{y^3}$

Step-by-step explanation:

1) Given that $x^{\frac{7}{4}}=(\sqrt{x^7})^\frac{1}{4}$

$x^{\frac{7}{4}}=\sqrt[4]{x^7}$ 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

$x^{\frac{7}{4}}=\sqrt[7]{x^4}$

2)Given that the rational exponent expression is $(729x^3y^{-18})^{\frac{1}{6}}$

To find it as a radical expression:

$(729x^3y^{-18})^{\frac{1}{6}}=(729)^{\frac{1}{6}}(x^3)^{\frac{1}{6}}((y^{-18})^{\frac{1}{6}})$

$=3(x^{\frac{3}{6}})(y^{\frac{-18}{6}})$

$=3(x^{\frac{1}{2}})(y^{-3})$

$=\frac{3\sqrt{x}}{y^3}$

Therefore $(729x^3y^{-18})^{\frac{1}{6}}=\frac{3\sqrt{x}}{y^3}$

Therefore Option A) is correct

That is $(729x^3y^{-18})^{\frac{1}{6}}=\frac{3\sqrt{x}}{y^3}$