To simplify the expression
[tex]\[ \frac{x^5}{x^9} \][/tex]
we can use the properties of exponents. Specifically, when we divide like bases, we subtract the exponents:
[tex]\[ \frac{x^a}{x^b} = x^{a-b} \][/tex]
Here, \( a = 5 \) and \( b = 9 \), so we subtract the exponent in the denominator from the exponent in the numerator:
[tex]\[ \frac{x^5}{x^9} = x^{5-9} \][/tex]
Simplifying the exponent:
[tex]\[ 5 - 9 = -4 \][/tex]
So the expression becomes:
[tex]\[ x^{-4} \][/tex]
This can also be written as:
[tex]\[ \frac{1}{x^4} \][/tex]
Thus, the simplified form of the expression \( \frac{x^5}{x^9} \) is:
[tex]\[ \frac{1}{x^4} \][/tex]
Among the given choices, the correct answer is:
[tex]\[ \boxed{\frac{1}{x^4}} \][/tex]
