Simplify Square Root Expression: √(x⁸/x¹⁰)

Solve the following exercise:

$\sqrt{\frac{x^8}{x^{10}}}=$

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 $\frac{1}{x}$.