Question

Use the rational exponent property to write an equivalent expression for 6√(n^5 - 2 + 1).

Answer 1

The sixth root of (n^5 - 2 + 1) using rational exponents is expressed as (n^5 - 2 + 1)^(1/6), applying the rule that the nth root of x can be written as x^(1/n).

Step-by-step explanation:

The student is asking how to write the sixth root of n raised to the fifth power minus two, plus one, using rational exponents. According to the rational exponent property, the expression 6√(n^5 - 2 + 1) can be written as (n^5 - 2 + 1)^(1/6). This is based on the rule that the nth root of a number x can be expressed as x raised to the power of 1/n.

For example, in rational exponent form, x squared, or x², is the same as the square root of x, which can be written as x to the power of 1/2 according to the equation x² = √x.