Solve Square Root of x⁴: Complete Step-by-Step Guide

Solve the following exercise:

$\sqrt{x^4}=$

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

a. The definition of root as an exponent:

$\sqrt[n]{a}=a^{\frac{1}{n}}$

b. Law of exponents for power to a power:

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

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

$\sqrt{x^4}= \\ \downarrow\\ (x^4)^{\frac{1}{2}}=$Let's continue, using the law of exponents mentioned in b to perform the exponentiation of the term in parentheses:

$(x^4)^{{\frac{1}{2}}} = \\ x^{4\cdot\frac{1}{2}}=\\ \boxed{x^2}$Therefore, the correct answer is answer b.