Question

find the value of 1/(1cube + 2 cube + 3cube)power -3/2

Answer 1

Ans.

$\frac{1}{( { {1}^{3} + {2}^{3} + {3}^{3} })^{ - \frac{ 3}{2} } } \\ = \frac{1}{ ({1 + 8 + 27)}^{ - \frac{3}{2} } } \\ = \frac{1}{ {(36)}^{ - \frac{3}{2} } } \\ = {(36)}^{ \frac{3}{2} } \\ = {(36)}^{1 + \frac{1}{2} } \\ = {36}^{1} \times {36}^{ \frac{1}{2} } \\ = 36 \times \sqrt{36} \\ = 36 \times 6 \\ = 216$

I HOPE THAT THIS HELPS YOU.

Answer 2

1/(1³+2³+3³)power-3/2

1/(1+8+27)power-3/2

1/36 power-3/2

As power is negative
So 1/36 will become 36.

36(³/²)
6²*³/²
6³

=216