Solve {left(1^3+2^3+3^3right)}^frac{3{2}}

$${ \left( { 1 }^{ 3 } + { 2 }^{ 3 } + { 3 }^{ 3 } \right) }^{ \frac{ 3 }{ 2 } }$$

Evaluate

$$216$$

Solution Steps

Calculate 1 to the power of 3 and get 1.

$$\left(1+2^{3}+3^{3}\right)^{\frac{3}{2}}$$

Calculate 2 to the power of 3 and get 8.

$$\left(1+8+3^{3}\right)^{\frac{3}{2}}$$

Add 1 and 8 to get 9.

$$\left(9+3^{3}\right)^{\frac{3}{2}}$$

Calculate 3 to the power of 3 and get 27.

$$\left(9+27\right)^{\frac{3}{2}}$$

Add 9 and 27 to get 36.

$$36^{\frac{3}{2}}$$

Calculate 36 to the power of \frac{3}{2} and get 216.

$$216$$

Factor

$$2^{3}\times 3^{3}$$