Question

What is the radical form of each of the given expressions?

What is the radical form of each of the given expressions?

6 1/5

6 7/5

6 1/6

7 1/2

7 5/2

6 9/2

Answer 1

`6^{(1)/(5) }=\sqrt[5]{6}`

`6^{(7)/(5) }=\sqrt[5]{6^7}`

`6^{(1)/(6) }=\sqrt[6]{6}`

`7^{(1)/(2) }=\sqrt[2]{7}`

`7^{(5)/(2) }=\sqrt[2]{7^5}`

`6^{(9)/(2) }=\sqrt[2]{6^9}`

Explanation:

A radical is the root operation for n roots such as square root or cuberoot in the form
`\sqrt[n]{x}`. A fraction exponent
`x^(m/n)` can be converted to the radical form.

`6^{(1)/(5) }=\sqrt[5]{6}`

`6^{(7)/(5) }=\sqrt[5]{6^7}`

`6^{(1)/(6) }=\sqrt[6]{6}`

`7^{(1)/(2) }=\sqrt[2]{7}`

`7^{(5)/(2) }=\sqrt[2]{7^5}`

`6^{(9)/(2) }=\sqrt[2]{6^9}`