Question

simplify: (\frac{x^{2}y^{5}}{x^{9}y^{5}}) options: (7^x), (\frac{1}{x^2}), (\frac{1}{x^7}) (and a fourth option partially visible)

Explanation:

Step1: Split into variable fractions

$\frac{x^2 y^5}{x^9 y^5} = \frac{x^2}{x^9} \times \frac{y^5}{y^5}$

Step2: Simplify y-term fraction

$\frac{y^5}{y^5} = 1$

Step3: Apply exponent rule to x-terms

$\frac{x^2}{x^9} = x^{2-9} = x^{-7} = \frac{1}{x^7}$

Step4: Multiply simplified terms

$\frac{1}{x^7} \times 1 = \frac{1}{x^7}$

Answer:

$\frac{1}{x^7}$