Question

which expression is equivalent to $\frac{9^{-4}}{3^{-4}}$?3$\frac{1}{3^{-4}}LXB03^{0}$

Explanation:

Step1: Rewrite 9 as power of 3

$9 = 3^2$, so $9^{-4} = (3^2)^{-4}$

Step2: Simplify the exponent

$(3^2)^{-4} = 3^{2 \times (-4)} = 3^{-8}$

Step3: Apply quotient rule of exponents

$\frac{3^{-8}}{3^{-4}} = 3^{-8 - (-4)} = 3^{-4 + 8} = 3^{4}$

Step4: Match to option form

$3^4 = \frac{1}{3^{-4}}$

Answer:

$\frac{1}{3^{-4}}$