a) ⁵√7³ * 7^{3/5} = 7^{3/5} * 7^{3/5} = 7^{3/5 + 3/5} = 7^{6/5} = 7^{1 + 1/5} = 7^{1} * 7^{1/5} = 7 * ⁵√7
b) [⁶√(⁷√7) * ⁷√7]/³√7 = [(7^{1/7})^{1/6} * 7^{1/7}]/7^{1/3} = [7^{1/42} * 7^{1/7}]/7^{1/3} = [7^{1/42 + 1/7}]/7^{1/3} = [7^{7/42}]/7^{1/3} = [7^{1/6}]/7^{2/6} = 7^{1/6 - 2/6} = 7^{- 1/6} = 1/⁶√7
c) 2^{2,5} * 16^{-0,5} = 2^{2,5} * 2^{-2} = 2^{2,5 - 2} = 2^{0,5} = √2 = 2/√2
d) [4 * (⁸√2)^{-1}]/[⁶√8 * √√2] = [2^{2} * 2{-1/8}]/[2^{3/6} * 2^{1/2 * 1/2}] = [2^{2} * 2{-1/8}]/[2^{1/2} * 2^{1/4}] = [2^{15/8}]/[2^{3/4} = 2^{9/8} = (1/2)^{-9/8} = (1/2)^{-1,125}
e) 8^{0,25} : ⁴√2 = 2^{3 * 0,25} : 2^{1/4} = 2^{0,75} * 2^{-1/4} = 2^{1/2} = 4^{1/4}
f) [2^{-3,3}]/[2^{-1,7}] = 2^{- 3,3 + 1,7} = 2^{-1,6} = 2^{-2 + 0,4} = (1/2)^{2} * 2^{2/5} = 0,25 * ⁵√4
g) 4^{-0,05} : 4^{1/5} = 4^{-1/20} * 4^{-1/5} = 4^{- 1/20 - 4/20} = 4^{- 5/20} = 4^{- 1/4} = 2^{- 2/4} = 2^{- 1/2} = 1/√2 = √2/2
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