Solve (3.545*10^-7)^7/(5.07*10^10)^11

$$\frac { ( 3.545 \times 10 ^ { - 7 } ) ^ { 7 } } { ( 5.07 \times 10 ^ { 10 } ) ^ { 11 } }$$

Evaluate

$$\frac{90058279596528053869}{728278555792727958161039931191040000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000}\approx 1.236591121 \cdot 10^{-163}$$

Solution Steps

Calculate 10 to the power of -7 and get \frac{1}{10000000}.

$$\frac{\left(3.545\times \frac{1}{10000000}\right)^{7}}{\left(5.07\times 10^{10}\right)^{11}}$$

Multiply 3.545 and \frac{1}{10000000} to get \frac{709}{2000000000}.

$$\frac{\left(\frac{709}{2000000000}\right)^{7}}{\left(5.07\times 10^{10}\right)^{11}}$$

Calculate \frac{709}{2000000000} to the power of 7 and get \frac{90058279596528053869}{128000000000000000000000000000000000000000000000000000000000000000}.

$$\frac{\frac{90058279596528053869}{128000000000000000000000000000000000000000000000000000000000000000}}{\left(5.07\times 10^{10}\right)^{11}}$$

Calculate 10 to the power of 10 and get 10000000000.

$$\frac{\frac{90058279596528053869}{128000000000000000000000000000000000000000000000000000000000000000}}{\left(5.07\times 10000000000\right)^{11}}$$

Multiply 5.07 and 10000000000 to get 50700000000.

$$\frac{\frac{90058279596528053869}{128000000000000000000000000000000000000000000000000000000000000000}}{50700000000^{11}}$$

Calculate 50700000000 to the power of 11 and get 5689676217130687173133124462430000000000000000000000000000000000000000000000000000000000000000000000000000000000000000.

$$\frac{\frac{90058279596528053869}{128000000000000000000000000000000000000000000000000000000000000000}}{5689676217130687173133124462430000000000000000000000000000000000000000000000000000000000000000000000000000000000000000}$$

Express \frac{\frac{90058279596528053869}{128000000000000000000000000000000000000000000000000000000000000000}}{5689676217130687173133124462430000000000000000000000000000000000000000000000000000000000000000000000000000000000000000} as a single fraction.

$$\frac{90058279596528053869}{128000000000000000000000000000000000000000000000000000000000000000\times 5689676217130687173133124462430000000000000000000000000000000000000000000000000000000000000000000000000000000000000000}$$

Multiply 128000000000000000000000000000000000000000000000000000000000000000 and 5689676217130687173133124462430000000000000000000000000000000000000000000000000000000000000000000000000000000000000000 to get 728278555792727958161039931191040000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000.

$$\frac{90058279596528053869}{728278555792727958161039931191040000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000}$$

Factor

$$\frac{709 ^ {7}}{2 ^ {158} \cdot 3 ^ {11} \cdot 5 ^ {151} \cdot 13 ^ {22}} = 1.236591121353285 \times 10^{-163}$$