Solve sqrt[5]{frac{1^{2}+2^{2}+3^3}{3^2+2^1+0^1}}

$$\sqrt[ 5 ] { \frac { 1 ^ { 2 } + 2 ^ { 2 } + 3 ^ { 3 } } { 3 ^ { 2 } + 2 ^ { 1 } + 0 ^ { 1 } } }$$

Evaluate

$$\frac{2\times 11^{\frac{4}{5}}}{11}\approx 1.238087841$$

Solution Steps

Calculate 1 to the power of 2 and get 1.

$$\sqrt[5]{\frac{1+2^{2}+3^{3}}{3^{2}+2^{1}+0^{1}}}$$

Calculate 2 to the power of 2 and get 4.

$$\sqrt[5]{\frac{1+4+3^{3}}{3^{2}+2^{1}+0^{1}}}$$

Add 1 and 4 to get 5.

$$\sqrt[5]{\frac{5+3^{3}}{3^{2}+2^{1}+0^{1}}}$$

Calculate 3 to the power of 3 and get 27.

$$\sqrt[5]{\frac{5+27}{3^{2}+2^{1}+0^{1}}}$$

Add 5 and 27 to get 32.

$$\sqrt[5]{\frac{32}{3^{2}+2^{1}+0^{1}}}$$

Calculate 3 to the power of 2 and get 9.

$$\sqrt[5]{\frac{32}{9+2^{1}+0^{1}}}$$

Calculate 2 to the power of 1 and get 2.

$$\sqrt[5]{\frac{32}{9+2+0^{1}}}$$

Add 9 and 2 to get 11.

$$\sqrt[5]{\frac{32}{11+0^{1}}}$$

Calculate 0 to the power of 1 and get 0.

$$\sqrt[5]{\frac{32}{11+0}}$$

Add 11 and 0 to get 11.

$$\sqrt[5]{\frac{32}{11}}$$