**Introduction**
The expression "root x 1/root x" can be simplified and understood by applying the rules of exponents and rational expressions. Let's break down the expression and explain it step by step.

**Simplifying the Expression**
To simplify the expression "root x 1/root x," we need to apply the rules of exponents and rational expressions.

**Understanding the Square Root**
The square root (√) of a number is a value that, when multiplied by itself, gives the original number. For example, √9 = 3 because 3 * 3 = 9.

**Applying the Rule of Exponents**
When we have the same base with different exponents, we can apply the rule of exponents to simplify the expression. In this case, the base is "x" and the exponents are 1/2 and -1.

**Rule 1: Product of Powers**
The rule states that when we multiply two numbers with the same base, we can add their exponents.

**Rule 2: Negative Exponent**
The rule states that any number raised to the power of -n is equal to 1 divided by the number raised to the power of n.

**Simplifying "root x"**
Let's simplify the expression "root x" first. Since the square root (√) can be represented as x^(1/2), we can rewrite "root x" as x^(1/2).

**Applying Rule 1**
Now, we can apply the rule of exponents to "root x 1/root x." Adding the exponents 1/2 and -1, we get x^(1/2) * x^(-1) = x^(1/2 - 1).

**Simplifying the Exponent**
To simplify further, we subtract the exponents: 1/2 - 1 = 1/2 - 2/2 = -1/2.

**Final Simplification**
Therefore, "root x 1/root x" simplifies to x^(-1/2), which can be expressed as 1/(root x). In other words, it is the reciprocal of the square root of x.

**Conclusion**
The expression "root x 1/root x" simplifies to 1/(root x) or x^(-1/2). By applying the rules of exponents and rational expressions, we can simplify complex expressions and understand their mathematical properties.