Solve 8(2*10^-3)^2/3(20)^5

$$\frac { 8 ( 2 \cdot 10 ^ { - 3 } ) ^ { 2 } } { 3 ( 20 ) ^ { 5 } }$$

Evaluate

$$\frac{1}{300000000000}\approx 3.333333333 \cdot 10^{-12}$$

Solution Steps

Calculate 10 to the power of -3 and get \frac{1}{1000}.

$$\frac{8\times \left(2\times \frac{1}{1000}\right)^{2}}{3\times 20^{5}}$$

Multiply 2 and \frac{1}{1000} to get \frac{1}{500}.

$$\frac{8\times \left(\frac{1}{500}\right)^{2}}{3\times 20^{5}}$$

Calculate \frac{1}{500} to the power of 2 and get \frac{1}{250000}.

$$\frac{8\times \frac{1}{250000}}{3\times 20^{5}}$$

Multiply 8 and \frac{1}{250000} to get \frac{1}{31250}.

$$\frac{\frac{1}{31250}}{3\times 20^{5}}$$

Calculate 20 to the power of 5 and get 3200000.

$$\frac{\frac{1}{31250}}{3\times 3200000}$$

Multiply 3 and 3200000 to get 9600000.

$$\frac{\frac{1}{31250}}{9600000}$$

Express \frac{\frac{1}{31250}}{9600000} as a single fraction.

$$\frac{1}{31250\times 9600000}$$

Multiply 31250 and 9600000 to get 300000000000.

$$\frac{1}{300000000000}$$

Factor

$$\frac{1}{2 ^ {11} \cdot 3 \cdot 5 ^ {11}} = 3.333333333333333 \times 10^{-12}$$