Question

1. simplify the expression below.

\\(\frac{9^{\frac{7}{4}}}{9^{\frac{9}{4}}}\\)

Explanation:

Step1: Apply exponent division rule

$\frac{9^{\frac{7}{4}}}{9^{\frac{9}{4}}} = 9^{\frac{7}{4}-\frac{9}{4}}$

Step2: Subtract the exponents

$9^{\frac{7-9}{4}} = 9^{-\frac{2}{4}} = 9^{-\frac{1}{2}}$

Step3: Rewrite negative exponent as reciprocal

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

Step4: Evaluate the positive exponent

$\frac{1}{9^{\frac{1}{2}}} = \frac{1}{\sqrt{9}} = \frac{1}{3}$

Answer:

$\frac{1}{3}$