Evaluate ( 2/3 )^(-3) · ( 3/4 )^(-3)

To evaluate ((frac{2}{3})^{-3} cdot (frac{3}{4})^{-3}), we will first simplify each term separately using the property of negative exponents, which states that (a^{-n} = frac{1}{a^n}).

1. Calculate ((frac{2}{3})^{-3}):

[

(frac{2}{3})^{-3} = frac{1}{(frac{2}{3})^3} = frac{1}{frac{2^3}{3^3}} = frac{3^3}{2^3} = frac{27}{8}

]

2. Calculate ((frac{3}{4})^{-3}):

[

(frac{3}{4})^{-3} = frac{1}{(frac{3}{4})^3} = frac{1}{frac{3^3}{4^3}} = frac{4^3}{3^3} = frac{64}{27}

]

3. Now, combine the results:

[

frac{27}{8} cdot frac{64}{27}

]

Here, the (27) in the numerator and denominator cancel out:

[

= frac{64}{8}

]

4. Finally