Square Root Simplification with Fractional Exponents

Video Solution

Solution Steps

00:00 Simplify the following problem

00:03 When there is a root of a fraction (A divided by B)

00:06 You can write it as a root of the numerator (A) divided by the root of the denominator (B)

00:09 Apply this formula to our exercise

00:17 Break down X to the power of 8 into X to the power of 4 squared

00:21 Break down X to the power of 4 into X squared squared

00:27 The root of any number (A) squared cancels out the square

00:31 Apply this formula to our exercise, and proceed to cancel out the squares:

00:45 Factor X to the power of 4 into X squared and X squared

00:49 Simplify wherever possible

00:53 This is the solution

Step-by-Step Solution

To solve this problem, we'll simplify the given expression step by step.

Firstly, observe the expression: $\sqrt{\frac{x^8}{x^4}}$ .

Step 1: Apply the quotient of powers rule: The expression inside the square root is $\frac{x^8}{x^4}$ , which simplifies to $x^{8-4} = x^4$ using the rule $\frac{x^m}{x^n} = x^{m-n}$ .
Step 2: Apply the square root rule: Now we have $\sqrt{x^4}$ . Utilizing the property of square roots, we find $\sqrt{x^4} = x^{4/2} = x^2$ .

Therefore, the simplified expression is $\textbf{x}^2$ .

Thus, the final solution to the problem is $\textbf{x}^2$ , which corresponds to choice 2 in the given list of options.