Resolver 2*250/0.05^2*(1,26*10^-6*frac{8*1,58{sqrt{125}*0.2})^2}

$$\frac { 2 \cdot 250 } { 0.05 ^ { 2 } \cdot ( 1,26 \cdot 10 ^ { - 6 } \cdot \frac { 8 \cdot 1,58 } { \sqrt { 125 } \cdot 0.2 } ) ^ { 2 } }$$

Calcular

$$\frac{97656250000000000000000}{24770529}\approx 3.942436998 \cdot 10^{15}$$

Pasos da solución

Multiplica 2 e 250 para obter 500.

$$\frac{500}{0.05^{2}\times \left(1.26\times 10^{-6}\times \frac{8\times 1.58}{0.2\sqrt{125}}\right)^{2}}$$

Calcula 0.05 á potencia de 2 e obtén 0.0025.

$$\frac{500}{0.0025\times \left(1.26\times 10^{-6}\times \frac{8\times 1.58}{0.2\sqrt{125}}\right)^{2}}$$

Calcula 10 á potencia de -6 e obtén \frac{1}{1000000}.

$$\frac{500}{0.0025\times \left(1.26\times \frac{1}{1000000}\times \frac{8\times 1.58}{0.2\sqrt{125}}\right)^{2}}$$

Multiplica 1.26 e \frac{1}{1000000} para obter \frac{63}{50000000}.

$$\frac{500}{0.0025\times \left(\frac{63}{50000000}\times \frac{8\times 1.58}{0.2\sqrt{125}}\right)^{2}}$$

Multiplica 8 e 1.58 para obter 12.64.

$$\frac{500}{0.0025\times \left(\frac{63}{50000000}\times \frac{12.64}{0.2\sqrt{125}}\right)^{2}}$$

Factoriza 125=5^{2}\times 5. Reescribe a raíz cadrada do produto \sqrt{5^{2}\times 5} como o produto de raíces cadradas \sqrt{5^{2}}\sqrt{5}. Obtén a raíz cadrada de 5^{2}.

$$\frac{500}{0.0025\times \left(\frac{63}{50000000}\times \frac{12.64}{0.2\times 5\sqrt{5}}\right)^{2}}$$

Multiplica 0.2 e 5 para obter 1.

$$\frac{500}{0.0025\times \left(\frac{63}{50000000}\times \frac{12.64}{\sqrt{5}}\right)^{2}}$$

Racionaliza o denominador de \frac{12.64}{\sqrt{5}} mediante a multiplicación do numerador e o denominador por \sqrt{5}.

$$\frac{500}{0.0025\times \left(\frac{63}{50000000}\times \frac{12.64\sqrt{5}}{\left(\sqrt{5}\right)^{2}}\right)^{2}}$$

O cadrado de \sqrt{5} é 5.

$$\frac{500}{0.0025\times \left(\frac{63}{50000000}\times \frac{12.64\sqrt{5}}{5}\right)^{2}}$$

Divide 12.64\sqrt{5} entre 5 para obter 2.528\sqrt{5}.

$$\frac{500}{0.0025\times \left(\frac{63}{50000000}\times 2.528\sqrt{5}\right)^{2}}$$

Multiplica \frac{63}{50000000} e 2.528 para obter \frac{4977}{1562500000}.

$$\frac{500}{0.0025\times \left(\frac{4977}{1562500000}\sqrt{5}\right)^{2}}$$

Expande \left(\frac{4977}{1562500000}\sqrt{5}\right)^{2}.

$$\frac{500}{0.0025\times \left(\frac{4977}{1562500000}\right)^{2}\left(\sqrt{5}\right)^{2}}$$

Calcula \frac{4977}{1562500000} á potencia de 2 e obtén \frac{24770529}{2441406250000000000}.

$$\frac{500}{0.0025\times \frac{24770529}{2441406250000000000}\left(\sqrt{5}\right)^{2}}$$

O cadrado de \sqrt{5} é 5.

$$\frac{500}{0.0025\times \frac{24770529}{2441406250000000000}\times 5}$$

Multiplica \frac{24770529}{2441406250000000000} e 5 para obter \frac{24770529}{488281250000000000}.

$$\frac{500}{0.0025\times \frac{24770529}{488281250000000000}}$$

Multiplica 0.0025 e \frac{24770529}{488281250000000000} para obter \frac{24770529}{195312500000000000000}.

$$\frac{500}{\frac{24770529}{195312500000000000000}}$$

Divide 500 entre \frac{24770529}{195312500000000000000} mediante a multiplicación de 500 polo recíproco de \frac{24770529}{195312500000000000000}.

$$500\times \frac{195312500000000000000}{24770529}$$

Multiplica 500 e \frac{195312500000000000000}{24770529} para obter \frac{97656250000000000000000}{24770529}.

$$\frac{97656250000000000000000}{24770529}$$

Factorizar

$$\frac{2 ^ {16} \cdot 5 ^ {26}}{3 ^ {4} \cdot 7 ^ {2} \cdot 79 ^ {2}} = 3942436998418564\frac{10952700}{24770529} = 3942436998418564.5$$