Question

the value of (1³+2³+3³+4³) power-3/2​

Answer 1

$\purple{ \begin{gathered}( { {1}^{3} + {2}^{3} + {3}^{3} })^{ \frac{1}{2} } \\ \\ = \: {((1 \times 1 \times 1) + (2 \times 2 \times 2)+ 3 \times (3 \times 3 \times 3))}^{ \frac{1}{2} } \\ \\ = {(1 + 8 + 27)}^{ \frac{1}{2} } \\ \\ = {36}^{ \frac{1}{2} } \\ \\ = {( {2}^{2} \times {3}^{2}) }^{ \frac{1}{2} } \\ \\ = ( {2}^{2 \times \frac{1}{2} } ) \times ( {3}^{2 \times \frac{1}{2} } ) \\ \\ = 2 \times 3 \\ \\ = 6 \\ \\ \end{gathered}}$