Solve sqrt[9]{1/5*10^6(500^9*10^4+400^9*{10}^5+{300}^9*{10}^6)}

$$\sqrt[ 9 ]{ \frac{ 1 }{ 5 \times { 10 }^{ 6 } } ( { 500 }^{ 9 } \times { 10 }^{ 4 } + { 400 }^{ 9 } \times { 10 }^{ 5 } + { 300 }^{ 9 } \times { 10 }^{ 6 } ) }$$

Evaluate

$$10\sqrt[9]{13085730000000}\approx 286.696238532$$

Solution Steps

Calculate 10 to the power of 6 and get 1000000.

$$\sqrt[9]{\frac{1}{5\times 1000000}\left(500^{9}\times 10^{4}+400^{9}\times 10^{5}+300^{9}\times 10^{6}\right)}$$

Multiply 5 and 1000000 to get 5000000.

$$\sqrt[9]{\frac{1}{5000000}\left(500^{9}\times 10^{4}+400^{9}\times 10^{5}+300^{9}\times 10^{6}\right)}$$

Calculate 500 to the power of 9 and get 1953125000000000000000000.

$$\sqrt[9]{\frac{1}{5000000}\left(1953125000000000000000000\times 10^{4}+400^{9}\times 10^{5}+300^{9}\times 10^{6}\right)}$$

Calculate 10 to the power of 4 and get 10000.

$$\sqrt[9]{\frac{1}{5000000}\left(1953125000000000000000000\times 10000+400^{9}\times 10^{5}+300^{9}\times 10^{6}\right)}$$

Multiply 1953125000000000000000000 and 10000 to get 19531250000000000000000000000.

$$\sqrt[9]{\frac{1}{5000000}\left(19531250000000000000000000000+400^{9}\times 10^{5}+300^{9}\times 10^{6}\right)}$$

Calculate 400 to the power of 9 and get 262144000000000000000000.

$$\sqrt[9]{\frac{1}{5000000}\left(19531250000000000000000000000+262144000000000000000000\times 10^{5}+300^{9}\times 10^{6}\right)}$$

Calculate 10 to the power of 5 and get 100000.

$$\sqrt[9]{\frac{1}{5000000}\left(19531250000000000000000000000+262144000000000000000000\times 100000+300^{9}\times 10^{6}\right)}$$

Multiply 262144000000000000000000 and 100000 to get 26214400000000000000000000000.

$$\sqrt[9]{\frac{1}{5000000}\left(19531250000000000000000000000+26214400000000000000000000000+300^{9}\times 10^{6}\right)}$$

Add 19531250000000000000000000000 and 26214400000000000000000000000 to get 45745650000000000000000000000.

$$\sqrt[9]{\frac{1}{5000000}\left(45745650000000000000000000000+300^{9}\times 10^{6}\right)}$$

Calculate 300 to the power of 9 and get 19683000000000000000000.

$$\sqrt[9]{\frac{1}{5000000}\left(45745650000000000000000000000+19683000000000000000000\times 10^{6}\right)}$$

Calculate 10 to the power of 6 and get 1000000.

$$\sqrt[9]{\frac{1}{5000000}\left(45745650000000000000000000000+19683000000000000000000\times 1000000\right)}$$

Multiply 19683000000000000000000 and 1000000 to get 19683000000000000000000000000.

$$\sqrt[9]{\frac{1}{5000000}\left(45745650000000000000000000000+19683000000000000000000000000\right)}$$

Add 45745650000000000000000000000 and 19683000000000000000000000000 to get 65428650000000000000000000000.

$$\sqrt[9]{\frac{1}{5000000}\times 65428650000000000000000000000}$$

Multiply \frac{1}{5000000} and 65428650000000000000000000000 to get 13085730000000000000000.

$$\sqrt[9]{13085730000000000000000}$$