Resolver left(100*10right)^-3sqrt{{left(2*2*10^340/36/15right)}^2+left(2*200*10^3right)^2}

$${ \left(100 \times 10 \right) }^{ -3 } \sqrt{ { \left( \frac{ 2 \cdot 2 \times 1 { 0 }^{ 3 } \frac{ 40 }{ 36 } }{ 15 } \right) }^{ 2 } + { \left(2 \cdot 200 \times { 10 }^{ 3 } \right) }^{ 2 } }$$

Calcular

$$\frac{1}{2500}=0.0004$$

Pasos da solución

Multiplica 100 e 10 para obter 1000.

$$1000^{-3}\sqrt{\left(\frac{2\times 2\times 1\times 0^{3}\times \frac{40}{36}}{15}\right)^{2}+\left(2\times 200\times 10^{3}\right)^{2}}$$

Calcula 1000 á potencia de -3 e obtén \frac{1}{1000000000}.

$$\frac{1}{1000000000}\sqrt{\left(\frac{2\times 2\times 1\times 0^{3}\times \frac{40}{36}}{15}\right)^{2}+\left(2\times 200\times 10^{3}\right)^{2}}$$

Multiplica 2 e 2 para obter 4.

$$\frac{1}{1000000000}\sqrt{\left(\frac{4\times 1\times 0^{3}\times \frac{40}{36}}{15}\right)^{2}+\left(2\times 200\times 10^{3}\right)^{2}}$$

Multiplica 4 e 1 para obter 4.

$$\frac{1}{1000000000}\sqrt{\left(\frac{4\times 0^{3}\times \frac{40}{36}}{15}\right)^{2}+\left(2\times 200\times 10^{3}\right)^{2}}$$

Calcula 0 á potencia de 3 e obtén 0.

$$\frac{1}{1000000000}\sqrt{\left(\frac{4\times 0\times \frac{40}{36}}{15}\right)^{2}+\left(2\times 200\times 10^{3}\right)^{2}}$$

Multiplica 4 e 0 para obter 0.

$$\frac{1}{1000000000}\sqrt{\left(\frac{0\times \frac{40}{36}}{15}\right)^{2}+\left(2\times 200\times 10^{3}\right)^{2}}$$

Reduce a fracción \frac{40}{36} a termos máis baixos extraendo e cancelando 4.

$$\frac{1}{1000000000}\sqrt{\left(\frac{0\times \frac{10}{9}}{15}\right)^{2}+\left(2\times 200\times 10^{3}\right)^{2}}$$

Multiplica 0 e \frac{10}{9} para obter 0.

$$\frac{1}{1000000000}\sqrt{\left(\frac{0}{15}\right)^{2}+\left(2\times 200\times 10^{3}\right)^{2}}$$

Cero dividido por calquera número distinto de cero dá cero.

$$\frac{1}{1000000000}\sqrt{0^{2}+\left(2\times 200\times 10^{3}\right)^{2}}$$

Calcula 0 á potencia de 2 e obtén 0.

$$\frac{1}{1000000000}\sqrt{0+\left(2\times 200\times 10^{3}\right)^{2}}$$

Multiplica 2 e 200 para obter 400.

$$\frac{1}{1000000000}\sqrt{0+\left(400\times 10^{3}\right)^{2}}$$

Calcula 10 á potencia de 3 e obtén 1000.

$$\frac{1}{1000000000}\sqrt{0+\left(400\times 1000\right)^{2}}$$

Multiplica 400 e 1000 para obter 400000.

$$\frac{1}{1000000000}\sqrt{0+400000^{2}}$$

Calcula 400000 á potencia de 2 e obtén 160000000000.

$$\frac{1}{1000000000}\sqrt{0+160000000000}$$

Suma 0 e 160000000000 para obter 160000000000.

$$\frac{1}{1000000000}\sqrt{160000000000}$$

Calcular a raíz cadrada de 160000000000 e obter 400000.

$$\frac{1}{1000000000}\times 400000$$

Multiplica \frac{1}{1000000000} e 400000 para obter \frac{1}{2500}.

$$\frac{1}{2500}$$

Factorizar

$$\frac{1}{2 ^ {2} \cdot 5 ^ {4}} = 0.0004$$