Simplify the Square Root: √(x^20/x^24) - Step-by-Step Solution

Solve the following exercise:

$\sqrt{\frac{x^{20}}{x^{24}}}=$

To solve this problem, we'll follow these steps:

• Simplify the expression inside the square root using exponent rules.
• Evaluate the square root of the simplified expression.

Let's work through the solution step-by-step:

First, simplify the expression inside the square root. We have:

$\frac{x^{20}}{x^{24}} = x^{20-24} = x^{-4}$

Next, apply the square root to the simplified expression:

$\sqrt{x^{-4}} = \left(x^{-4}\right)^{1/2} = x^{-4 \times \frac{1}{2}} = x^{-2}$

This can be written as:

$x^{-2} = \frac{1}{x^2}$

Therefore, the solution to the problem is $\frac{1}{x^2}$.