Solve frac{(9*10^{9})^{3}*(16*10^{-19})^6*9,1*10^-31}{(4,1*10^-34)^4}

$$\frac { ( 9 \cdot 10 ^ { 9 } ) ^ { 3 } \cdot ( 16 \cdot 10 ^ { - 19 } ) ^ { 6 } \cdot 9,1 \cdot 10 ^ { - 31 } } { ( 4,1 \cdot 10 ^ { - 34 } ) ^ { 4 } }$$

Evaluate

$$\frac{1112983732224000000000000000000000}{2825761}\approx 3,938704414 \cdot 10^{26}$$

Solution Steps

Calculate 10 to the power of 9 and get 1000000000.

$$\frac{\left(9\times 1000000000\right)^{3}\times \left(16\times 10^{-19}\right)^{6}\times 9,1\times 10^{-31}}{\left(4,1\times 10^{-34}\right)^{4}}$$

Multiply 9 and 1000000000 to get 9000000000.

$$\frac{9000000000^{3}\times \left(16\times 10^{-19}\right)^{6}\times 9,1\times 10^{-31}}{\left(4,1\times 10^{-34}\right)^{4}}$$

Calculate 9000000000 to the power of 3 and get 729000000000000000000000000000.

$$\frac{729000000000000000000000000000\times \left(16\times 10^{-19}\right)^{6}\times 9,1\times 10^{-31}}{\left(4,1\times 10^{-34}\right)^{4}}$$

Calculate 10 to the power of -19 and get \frac{1}{10000000000000000000}.

$$\frac{729000000000000000000000000000\times \left(16\times \frac{1}{10000000000000000000}\right)^{6}\times 9,1\times 10^{-31}}{\left(4,1\times 10^{-34}\right)^{4}}$$

Multiply 16 and \frac{1}{10000000000000000000} to get \frac{1}{625000000000000000}.

$$\frac{729000000000000000000000000000\times \left(\frac{1}{625000000000000000}\right)^{6}\times 9,1\times 10^{-31}}{\left(4,1\times 10^{-34}\right)^{4}}$$

Calculate \frac{1}{625000000000000000} to the power of 6 and get \frac{1}{59604644775390625000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000}.

$$\frac{729000000000000000000000000000\times \frac{1}{59604644775390625000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000}\times 9,1\times 10^{-31}}{\left(4,1\times 10^{-34}\right)^{4}}$$

Multiply 729000000000000000000000000000 and \frac{1}{59604644775390625000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000} to get \frac{729}{59604644775390625000000000000000000000000000000000000000000000000000000000000000}.

$$\frac{\frac{729}{59604644775390625000000000000000000000000000000000000000000000000000000000000000}\times 9,1\times 10^{-31}}{\left(4,1\times 10^{-34}\right)^{4}}$$

Multiply \frac{729}{59604644775390625000000000000000000000000000000000000000000000000000000000000000} and 9,1 to get \frac{66339}{596046447753906250000000000000000000000000000000000000000000000000000000000000000}.

$$\frac{\frac{66339}{596046447753906250000000000000000000000000000000000000000000000000000000000000000}\times 10^{-31}}{\left(4,1\times 10^{-34}\right)^{4}}$$

Calculate 10 to the power of -31 and get \frac{1}{10000000000000000000000000000000}.

$$\frac{\frac{66339}{596046447753906250000000000000000000000000000000000000000000000000000000000000000}\times \frac{1}{10000000000000000000000000000000}}{\left(4,1\times 10^{-34}\right)^{4}}$$

Multiply \frac{66339}{596046447753906250000000000000000000000000000000000000000000000000000000000000000} and \frac{1}{10000000000000000000000000000000} to get \frac{66339}{5960464477539062500000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000}.

$$\frac{\frac{66339}{5960464477539062500000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000}}{\left(4,1\times 10^{-34}\right)^{4}}$$

Calculate 10 to the power of -34 and get \frac{1}{10000000000000000000000000000000000}.

$$\frac{\frac{66339}{5960464477539062500000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000}}{\left(4,1\times \frac{1}{10000000000000000000000000000000000}\right)^{4}}$$

Multiply 4,1 and \frac{1}{10000000000000000000000000000000000} to get \frac{41}{100000000000000000000000000000000000}.

$$\frac{\frac{66339}{5960464477539062500000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000}}{\left(\frac{41}{100000000000000000000000000000000000}\right)^{4}}$$

Calculate \frac{41}{100000000000000000000000000000000000} to the power of 4 and get \frac{2825761}{100000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000}.

$$\frac{\frac{66339}{5960464477539062500000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000}}{\frac{2825761}{100000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000}}$$

Divide \frac{66339}{5960464477539062500000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000} by \frac{2825761}{100000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000} by multiplying \frac{66339}{5960464477539062500000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000} by the reciprocal of \frac{2825761}{100000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000}.

$$\frac{66339}{5960464477539062500000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000}\times \frac{100000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000}{2825761}$$

Multiply \frac{66339}{5960464477539062500000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000} and \frac{100000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000}{2825761} to get \frac{1112983732224000000000000000000000}{2825761}.

$$\frac{1112983732224000000000000000000000}{2825761}$$

Factor

$$\frac{7 \cdot 13 \cdot 2 ^ {45} \cdot 3 ^ {6} \cdot 5 ^ {21}}{41 ^ {4}} = 3.93870441351551 \times 10^{26}\frac{2221282}{2825761} = 3.93870441351551 \times 10^{26}$$