Simplify and express answers using positive exponents only. Variables are restricted to avoid division by 0 . \( \frac{x^{-11}}{x^{-4}} \) \( \frac{x^{-11}}{x^{-4}}=\square \) (Use positive exponents only.)

To simplify the expression \( \frac{x^{-11}}{x^{-4}} \), you use the property of exponents that states \( \frac{a^m}{a^n} = a^{m-n} \). Here, \( m = -11 \) and \( n = -4 \). So the calculation becomes: \( x^{-11 - (-4)} = x^{-11 + 4} = x^{-7} \). To express this using positive exponents, you would rewrite \( x^{-7} \) as \( \frac{1}{x^7} \). Thus, \( \frac{x^{-11}}{x^{-4}} = \frac{1}{x^7} \).