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Question

Mathematics Question on Laws of Exponents for Real Numbers

Find: (i) 9 32\frac{3}{2} (ii) 32 25\frac{2}{5} (iii) 16 34\frac{3}{4} (iv) 125 -13\frac{1}{3}

Answer

(i) 9 32\frac{3}{2} = (9 12\frac{1}{2})3 13\frac{1}{3}= (3)3 = 27

(ii) 32 25\frac{2}{5} = (32 15\frac{1}{5})2 = (2)2 = 4

(iii) 16 34\frac{3}{4} = (1614\frac{1}{4})3 = (2)3 = 8

(iv) 125 -13\frac{1}{3} = 1(125)13\frac{1}{(125)}\frac{1}{3} = 15\frac{1}{5}