Simplify Square Root Expression: √(x⁸/x¹⁰)

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 We can write it as the root of the numerator (A) divided by the root of the denominator (B)

00:09 Apply this formula to our exercise

00:14 Break down X to the power of 8 into X to the power of 4 squared

00:20 Break down X to the power of 10 into X to the power of 5 squared

00:25 The root of any number (A) squared cancels out the square

00:29 Apply this formula to our exercise and cancel out the squares

00:40 Break down X to the power of 5 into factors X to the power of 4 and X

00:48 Reduce wherever possible

00:51 This is the solution

Step-by-Step Solution

To solve this mathematical expression, follow these steps:

Step 1: Use the Quotient Property of Exponents

Simplify the expression inside the square root using the rule:
$\frac{x^8}{x^{10}} = x^{8-10} = x^{-2}$ .
Step 2: Apply the Square Root Property

Now, apply the square root:
$\sqrt{x^{-2}} = (x^{-2})^{1/2} = x^{-2 \cdot \frac{1}{2}} = x^{-1}$ .
Step 3: Express in Simpler Form

The expression $x^{-1}$ can be written as $\frac{1}{x}$ .

Therefore, the final simplified form of the expression is $\frac{1}{x}$ .