Question

Please help me very urgent

Answer 1

$(i) \: (3 \times 9) ^{ \frac{1}{2} } \times 9 ^{ \frac{3}{2} } \\ = (3 \times 3 \times 3) ^{ \frac{1}{2} } \times (3 \times 3)^{ \frac{3}{2} } \\ = ( {3}^{3} )^{ \frac{1}{2} } \times ( {3}^{2} )^{ \frac{3}{2} } \\ = {3}^{ \frac{3}{2} } \times {3}^{3} \\ = {3}^{ \frac{3}{2} + 3} \\ = {3}^{ \frac{3 + 6}{2} } \\ = {3}^{ \frac{9}{2} } \\(ii) \: ( {1}^{3} + {2}^{3} + {3}^{3} ) ^{ \frac{5}{2} } \\ = (1+ 8 + 27) ^{ \frac{5}{2} } \\ = (36) ^{ \frac{5}{2} } \\ = ( {6}^{2})^{ \frac{5}{2} } \\ = {6}^{5} \\ = 7776$