Question

simplify.
$9^{-\frac{1}{3}} cdot 3^{-\frac{1}{3}}$

Explanation:

Step1: Rewrite 9 as power of 3

$9^{-\frac{1}{3}} = (3^2)^{-\frac{1}{3}}$

Step2: Simplify exponent of 3

$(3^2)^{-\frac{1}{3}} = 3^{-\frac{2}{3}}$

Step3: Multiply like bases, add exponents

$3^{-\frac{2}{3}} \cdot 3^{-\frac{1}{3}} = 3^{-\frac{2}{3} + (-\frac{1}{3})}$

Step4: Calculate combined exponent

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

Step5: Rewrite negative exponent as reciprocal

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

Answer:

$\frac{1}{3}$