Вычислите: a) 16^(1/4); б) 8^(2/3); в) 3⁻² · 81^(1/4); г) 0,01^(-1/2); д) 64^(3/2) · 4⁻² · (80)⁻³.

a) $$16^{\frac{1}{4}} = (2^4)^{\frac{1}{4}} = 2^{4 \cdot \frac{1}{4}} = 2^1 = 2$$

б) $$8^{\frac{2}{3}} = (2^3)^{\frac{2}{3}} = 2^{3 \cdot \frac{2}{3}} = 2^2 = 4$$

в) $$3^{-2} \cdot 81^{\frac{1}{4}} = \frac{1}{3^2} \cdot (3^4)^{\frac{1}{4}} = \frac{1}{9} \cdot 3^{4 \cdot \frac{1}{4}} = \frac{1}{9} \cdot 3 = \frac{3}{9} = \frac{1}{3}$$

г) $$0.01^{-\frac{1}{2}} = (\frac{1}{100})^{-\frac{1}{2}} = (\frac{1}{10^2})^{-\frac{1}{2}} = (10^{-2})^{-\frac{1}{2}} = 10^{-2 \cdot (-\frac{1}{2})} = 10^1 = 10$$

д) $$64^{\frac{3}{2}} \cdot 4^{-2} \cdot (80)^{-3} = (8^2)^{\frac{3}{2}} \cdot (2^2)^{-2} \cdot (2^4 \cdot 5)^{-3} = 8^{2 \cdot \frac{3}{2}} \cdot 2^{-4} \cdot (2^4)^{-3} \cdot 5^{-3} = 8^3 \cdot 2^{-4} \cdot 2^{-12} \cdot 5^{-3} = 512 \cdot 2^{-16} \cdot 5^{-3} = 2^9 \cdot 2^{-16} \cdot 5^{-3} = 2^{-7} \cdot 5^{-3} = \frac{1}{2^7} \cdot \frac{1}{5^3} = \frac{1}{128} \cdot \frac{1}{125} = \frac{1}{16000}$$