Evaluate.
( 2/3 )^(-3) · ( 3/4 )^(-3)
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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