Question

NEED HELP ASAP 70 POINTS

1.Which of the following rational exponent expressions is NOT simplified correctly as a radical expression?
2. Simplify the rational exponent expression as a radical expression. (729x^3y^-18)^1/6
*Answer choices in linked pics*

Answer 1

1) Option A) is correct

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

`x^{(7)/(4)}=\sqrt[7]{x^4}`

2)Option A) is correct

That is
`(729x^3y^(-18))^{(1)/(6)}=(3√(x))/(y^3)`

Explanation:

1) Given that
`x^{(7)/(4)}=(√(x^7))^(1)/(4)`

`x^{(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^{(7)/(4)}=\sqrt[7]{x^4}`

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

To find it as a radical expression:

`(729x^3y^(-18))^{(1)/(6)}=(729)^{(1)/(6)}(x^3)^{(1)/(6)}((y^(-18))^{(1)/(6)})`

`=3(x^{(3)/(6)})(y^{(-18)/(6)})`

`=3(x^{(1)/(2)})(y^(-3))`

`=(3√(x))/(y^3)`

Therefore
`(729x^3y^(-18))^{(1)/(6)}=(3√(x))/(y^3)`

Therefore Option A) is correct

That is
`(729x^3y^(-18))^{(1)/(6)}=(3√(x))/(y^3)`