Solve frac{8,99*10^{9}N*m^{2}/c^2(3,4*10^-5c)(5,10^-7c)}{(0,03m)^2}

$$\frac { 8,99 \cdot 10 ^ { 9 } N \cdot m ^ { 2 } / c ^ { 2 } ( 3,4 \cdot 10 ^ { - 5 } c ) ( 5,10 ^ { - 7 } c ) } { ( 0,03 m ) ^ { 2 } }$$

Evaluate

$$\frac{1798000000000000N}{475099770627}$$

Solution Steps

Multiply c and c to get c^{2}.

$$\frac{\frac{8.99\times 10^{9}Nm^{2}}{c^{2}}\times 3.4\times 10^{-5}c^{2}\times 5.1^{-7}}{\left(0.03m\right)^{2}}$$

Calculate 10 to the power of 9 and get 1000000000.

$$\frac{\frac{8.99\times 1000000000Nm^{2}}{c^{2}}\times 3.4\times 10^{-5}c^{2}\times 5.1^{-7}}{\left(0.03m\right)^{2}}$$

Multiply 8.99 and 1000000000 to get 8990000000.

$$\frac{\frac{8990000000Nm^{2}}{c^{2}}\times 3.4\times 10^{-5}c^{2}\times 5.1^{-7}}{\left(0.03m\right)^{2}}$$

Calculate 10 to the power of -5 and get \frac{1}{100000}.

$$\frac{\frac{8990000000Nm^{2}}{c^{2}}\times 3.4\times \frac{1}{100000}c^{2}\times 5.1^{-7}}{\left(0.03m\right)^{2}}$$

Multiply 3.4 and \frac{1}{100000} to get \frac{17}{500000}.

$$\frac{\frac{8990000000Nm^{2}}{c^{2}}\times \frac{17}{500000}c^{2}\times 5.1^{-7}}{\left(0.03m\right)^{2}}$$

Calculate 5.1 to the power of -7 and get \frac{10000000}{897410677851}.

$$\frac{\frac{8990000000Nm^{2}}{c^{2}}\times \frac{17}{500000}c^{2}\times \frac{10000000}{897410677851}}{\left(0.03m\right)^{2}}$$

Multiply \frac{17}{500000} and \frac{10000000}{897410677851} to get \frac{20}{52788863403}.

$$\frac{\frac{8990000000Nm^{2}}{c^{2}}\times \frac{20}{52788863403}c^{2}}{\left(0.03m\right)^{2}}$$

Multiply \frac{8990000000Nm^{2}}{c^{2}} times \frac{20}{52788863403} by multiplying numerator times numerator and denominator times denominator.

$$\frac{\frac{8990000000Nm^{2}\times 20}{c^{2}\times 52788863403}c^{2}}{\left(0.03m\right)^{2}}$$

Express \frac{8990000000Nm^{2}\times 20}{c^{2}\times 52788863403}c^{2} as a single fraction.

$$\frac{\frac{8990000000Nm^{2}\times 20c^{2}}{c^{2}\times 52788863403}}{\left(0.03m\right)^{2}}$$

Cancel out c^{2} in both numerator and denominator.

$$\frac{\frac{20\times 8990000000Nm^{2}}{52788863403}}{\left(0.03m\right)^{2}}$$

Expand \left(0.03m\right)^{2}.

$$\frac{\frac{20\times 8990000000Nm^{2}}{52788863403}}{0.03^{2}m^{2}}$$

Calculate 0.03 to the power of 2 and get 0.0009.

$$\frac{\frac{20\times 8990000000Nm^{2}}{52788863403}}{0.0009m^{2}}$$

Express \frac{\frac{20\times 8990000000Nm^{2}}{52788863403}}{0.0009m^{2}} as a single fraction.

$$\frac{20\times 8990000000Nm^{2}}{52788863403\times 0.0009m^{2}}$$

Cancel out m^{2} in both numerator and denominator.

$$\frac{20\times 8990000000N}{0.0009\times 52788863403}$$

Multiply 20 and 8990000000 to get 179800000000.

$$\frac{179800000000N}{0.0009\times 52788863403}$$

Multiply 0.0009 and 52788863403 to get 47509977.0627.

$$\frac{179800000000N}{47509977.0627}$$

Divide 179800000000N by 47509977.0627 to get \frac{1798000000000000}{475099770627}N.

$$\frac{1798000000000000}{475099770627}N$$

Expand

$$\frac{1798000000000000N}{475099770627}$$

Solution Steps

Multiply c and c to get c^{2}.

$$\frac{\frac{8.99\times 10^{9}Nm^{2}}{c^{2}}\times 3.4\times 10^{-5}c^{2}\times 5.1^{-7}}{\left(0.03m\right)^{2}}$$

Calculate 10 to the power of 9 and get 1000000000.

$$\frac{\frac{8.99\times 1000000000Nm^{2}}{c^{2}}\times 3.4\times 10^{-5}c^{2}\times 5.1^{-7}}{\left(0.03m\right)^{2}}$$

Multiply 8.99 and 1000000000 to get 8990000000.

$$\frac{\frac{8990000000Nm^{2}}{c^{2}}\times 3.4\times 10^{-5}c^{2}\times 5.1^{-7}}{\left(0.03m\right)^{2}}$$

Calculate 10 to the power of -5 and get \frac{1}{100000}.

$$\frac{\frac{8990000000Nm^{2}}{c^{2}}\times 3.4\times \frac{1}{100000}c^{2}\times 5.1^{-7}}{\left(0.03m\right)^{2}}$$

Multiply 3.4 and \frac{1}{100000} to get \frac{17}{500000}.

$$\frac{\frac{8990000000Nm^{2}}{c^{2}}\times \frac{17}{500000}c^{2}\times 5.1^{-7}}{\left(0.03m\right)^{2}}$$

Calculate 5.1 to the power of -7 and get \frac{10000000}{897410677851}.

$$\frac{\frac{8990000000Nm^{2}}{c^{2}}\times \frac{17}{500000}c^{2}\times \frac{10000000}{897410677851}}{\left(0.03m\right)^{2}}$$

Multiply \frac{17}{500000} and \frac{10000000}{897410677851} to get \frac{20}{52788863403}.

$$\frac{\frac{8990000000Nm^{2}}{c^{2}}\times \frac{20}{52788863403}c^{2}}{\left(0.03m\right)^{2}}$$

Multiply \frac{8990000000Nm^{2}}{c^{2}} times \frac{20}{52788863403} by multiplying numerator times numerator and denominator times denominator.

$$\frac{\frac{8990000000Nm^{2}\times 20}{c^{2}\times 52788863403}c^{2}}{\left(0.03m\right)^{2}}$$

Express \frac{8990000000Nm^{2}\times 20}{c^{2}\times 52788863403}c^{2} as a single fraction.

$$\frac{\frac{8990000000Nm^{2}\times 20c^{2}}{c^{2}\times 52788863403}}{\left(0.03m\right)^{2}}$$

Cancel out c^{2} in both numerator and denominator.

$$\frac{\frac{20\times 8990000000Nm^{2}}{52788863403}}{\left(0.03m\right)^{2}}$$

Expand \left(0.03m\right)^{2}.

$$\frac{\frac{20\times 8990000000Nm^{2}}{52788863403}}{0.03^{2}m^{2}}$$

Calculate 0.03 to the power of 2 and get 0.0009.

$$\frac{\frac{20\times 8990000000Nm^{2}}{52788863403}}{0.0009m^{2}}$$

Express \frac{\frac{20\times 8990000000Nm^{2}}{52788863403}}{0.0009m^{2}} as a single fraction.

$$\frac{20\times 8990000000Nm^{2}}{52788863403\times 0.0009m^{2}}$$

Cancel out m^{2} in both numerator and denominator.

$$\frac{20\times 8990000000N}{0.0009\times 52788863403}$$

Multiply 20 and 8990000000 to get 179800000000.

$$\frac{179800000000N}{0.0009\times 52788863403}$$

Multiply 0.0009 and 52788863403 to get 47509977.0627.

$$\frac{179800000000N}{47509977.0627}$$

Divide 179800000000N by 47509977.0627 to get \frac{1798000000000000}{475099770627}N.

$$\frac{1798000000000000}{475099770627}N$$