Resolver 6*62*6*10^-24/sqrt{2*167*10^-27*81*9*10^-16}

$$\frac { 6 \cdot 62 \cdot 6 \times 10 ^ { - 24 } } { \sqrt { 2 \times 167 \times 10 ^ { - 27 } \times 81 \cdot 9 \times 10 ^ { - 16 } } }$$

Avaliar

$$\frac{31\sqrt{835}}{62625}\approx 0,01430399$$

Passos Para a Resolução

Para multiplicar as potências da mesma base, some os seus expoentes. Some -27 e -16 para obter -43.

$$\frac{6\times 62\times 6\times 10^{-24}}{\sqrt{2\times 167\times 10^{-43}\times 81\times 9}}$$

Multiplique 6 e 62 para obter 372.

$$\frac{372\times 6\times 10^{-24}}{\sqrt{2\times 167\times 10^{-43}\times 81\times 9}}$$

Multiplique 372 e 6 para obter 2232.

$$\frac{2232\times 10^{-24}}{\sqrt{2\times 167\times 10^{-43}\times 81\times 9}}$$

Calcule 10 elevado a -24 e obtenha \frac{1}{1000000000000000000000000}.

$$\frac{2232\times \frac{1}{1000000000000000000000000}}{\sqrt{2\times 167\times 10^{-43}\times 81\times 9}}$$

Multiplique 2232 e \frac{1}{1000000000000000000000000} para obter \frac{279}{125000000000000000000000}.

$$\frac{\frac{279}{125000000000000000000000}}{\sqrt{2\times 167\times 10^{-43}\times 81\times 9}}$$

Multiplique 2 e 167 para obter 334.

$$\frac{\frac{279}{125000000000000000000000}}{\sqrt{334\times 10^{-43}\times 81\times 9}}$$

Calcule 10 elevado a -43 e obtenha \frac{1}{10000000000000000000000000000000000000000000}.

$$\frac{\frac{279}{125000000000000000000000}}{\sqrt{334\times \frac{1}{10000000000000000000000000000000000000000000}\times 81\times 9}}$$

Multiplique 334 e \frac{1}{10000000000000000000000000000000000000000000} para obter \frac{167}{5000000000000000000000000000000000000000000}.

$$\frac{\frac{279}{125000000000000000000000}}{\sqrt{\frac{167}{5000000000000000000000000000000000000000000}\times 81\times 9}}$$

Multiplique \frac{167}{5000000000000000000000000000000000000000000} e 81 para obter \frac{13527}{5000000000000000000000000000000000000000000}.

$$\frac{\frac{279}{125000000000000000000000}}{\sqrt{\frac{13527}{5000000000000000000000000000000000000000000}\times 9}}$$

Multiplique \frac{13527}{5000000000000000000000000000000000000000000} e 9 para obter \frac{121743}{5000000000000000000000000000000000000000000}.

$$\frac{\frac{279}{125000000000000000000000}}{\sqrt{\frac{121743}{5000000000000000000000000000000000000000000}}}$$

Reescreva a raiz quadrada da divisão \sqrt{\frac{121743}{5000000000000000000000000000000000000000000}} à medida que a divisão de raízes quadradas \frac{\sqrt{121743}}{\sqrt{5000000000000000000000000000000000000000000}}.

$$\frac{\frac{279}{125000000000000000000000}}{\frac{\sqrt{121743}}{\sqrt{5000000000000000000000000000000000000000000}}}$$

Fatorize a expressão 121743=27^{2}\times 167. Reescreva a raiz quadrada do produto \sqrt{27^{2}\times 167} à medida que o produto das raízes quadradas \sqrt{27^{2}}\sqrt{167}. Calcule a raiz quadrada de 27^{2}.

$$\frac{\frac{279}{125000000000000000000000}}{\frac{27\sqrt{167}}{\sqrt{5000000000000000000000000000000000000000000}}}$$

Fatorize a expressão 5000000000000000000000000000000000000000000=1000000000000000000000^{2}\times 5. Reescreva a raiz quadrada do produto \sqrt{1000000000000000000000^{2}\times 5} à medida que o produto das raízes quadradas \sqrt{1000000000000000000000^{2}}\sqrt{5}. Calcule a raiz quadrada de 1000000000000000000000^{2}.

$$\frac{\frac{279}{125000000000000000000000}}{\frac{27\sqrt{167}}{1000000000000000000000\sqrt{5}}}$$

Racionalize o denominador de \frac{27\sqrt{167}}{1000000000000000000000\sqrt{5}} ao multiplicar o numerador e o denominador por \sqrt{5}.

$$\frac{\frac{279}{125000000000000000000000}}{\frac{27\sqrt{167}\sqrt{5}}{1000000000000000000000\left(\sqrt{5}\right)^{2}}}$$

O quadrado de \sqrt{5} é 5.

$$\frac{\frac{279}{125000000000000000000000}}{\frac{27\sqrt{167}\sqrt{5}}{1000000000000000000000\times 5}}$$

Para multiplicar \sqrt{167} e \sqrt{5}, multiplique os números sob a raiz quadrada.

$$\frac{\frac{279}{125000000000000000000000}}{\frac{27\sqrt{835}}{1000000000000000000000\times 5}}$$

Multiplique 1000000000000000000000 e 5 para obter 5000000000000000000000.

$$\frac{\frac{279}{125000000000000000000000}}{\frac{27\sqrt{835}}{5000000000000000000000}}$$

Divida \frac{279}{125000000000000000000000} por \frac{27\sqrt{835}}{5000000000000000000000} ao multiplicar \frac{279}{125000000000000000000000} pelo recíproco de \frac{27\sqrt{835}}{5000000000000000000000}.

$$\frac{279\times 5000000000000000000000}{125000000000000000000000\times 27\sqrt{835}}$$

Anule 9\times 5000000000000000000000 no numerador e no denominador.

$$\frac{31}{3\times 25\sqrt{835}}$$

Racionalize o denominador de \frac{31}{3\times 25\sqrt{835}} ao multiplicar o numerador e o denominador por \sqrt{835}.

$$\frac{31\sqrt{835}}{3\times 25\left(\sqrt{835}\right)^{2}}$$

O quadrado de \sqrt{835} é 835.

$$\frac{31\sqrt{835}}{3\times 25\times 835}$$

Multiplique 3 e 25 para obter 75.

$$\frac{31\sqrt{835}}{75\times 835}$$

Multiplique 75 e 835 para obter 62625.

$$\frac{31\sqrt{835}}{62625}$$