Square Root Simplification with Fractional Exponents

Video Solution

Solution Steps

00:10 Let's simplify this problem together.

00:13 When you have a root of a fraction, like A over B.

00:17 You can think of it as the root of A, over the root of B.

00:22 Now, let's use this idea in our exercise.

00:27 First, change X to the power of 8, into X to the power of 4 squared.

00:32 Next, turn X to the power of 4, into X squared squared.

00:38 Remember, the root of A squared, cancels out the square.

00:43 Now, apply this to cancel the squares in our exercise.

00:55 Break X to the power of 4 into X squared times X squared.

01:00 Simplify everything you can.

01:03 And that's our solution! Great job!

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.