Solve the Square Root Expression: Simplifying √x²

In order to simplify the given expression, we will use two laws of exponents:

a. The definition of root as an exponent:

$\sqrt[n]{a}=a^{\frac{1}{n}}$b. The law of exponents for power of a power:

$(a^m)^n=a^{m\cdot n}$

Let's start with converting the square root to an exponent using the law mentioned in a':

$\sqrt{x^2}= \\ \downarrow\\ (x^2)^{\frac{1}{2}}=$We'll continue using the law of exponents mentioned in b' and perform the exponent operation on the term in parentheses:

$(x^2)^{\frac{1}{2}}= \\ x^{2\cdot\frac{1}{2}}\\ x^1=\\ \boxed{x}$Therefore, the correct answer is answer a'.