Use the rational exponent property to write an equivalent expression for \sqrt[5]{n ^(4) } + 3 - 12 ​

Question

Use the rational exponent property to write an equivalent expression for


`\sqrt[5]{n ^(4) } + 3 - 12`
​

Answer 1

For this case we have that by definition, a rational exponent is an exponent that can be expressed as
`\frac {a} {b}`, where a and b are integers and n is nonzero.

The exponent
`\frac {1} {a}` indicates the "a" root.
`x ^ {\frac {1} {a}} = \sqrt [a] {x}`

We have the following expression:

`\sqrt [5] {n ^ 4} + 3-12 =`

Different signs are subtracted and the sign of the major is placed:

`\sqrt [5] {n ^ 4} -9 =`

Applying the property:

`n ^ {\frac {4} {5}} - 9`

Answer:

`n ^ {\frac {4} {5}} - 9`