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Question

Mathematics Question on Laws of Exponents for Real Numbers

Find: (i) 64 12\frac{1}{2} (ii) 32 12\frac{1}{2} (iii) 125 13\frac{1}{3}

Answer

(i) 64 12\frac{1}{2} = (8)2 12\frac{1}{2}

= 8

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

= 2

(iii) 12513\frac{1}{3} = (5 × 5 × 5) 13\frac{1}{3}= 53 (13)(\frac{1}{3})

= 5