Solve frac{(9*10^{9}Nm^{2}/c^2)(1.0*10^-2c^-2)}{(3.10m)^2}

$$\frac { ( 9 \times 10 ^ { 9 } Nm ^ { 2 } / c ^ { 2 } ) ( 1.0 \times 10 ^ { - 2 } c ^ { - 2 } ) } { ( 3.10 m ) ^ { 2 } }$$

Evaluate

$$\frac{9000000000N}{961c^{4}}$$

Solution Steps

Calculate 10 to the power of 9 and get 1000000000.

$$\frac{\frac{9\times 1000000000Nm^{2}}{c^{2}}\times 1\times 10^{-2}c^{-2}}{\left(3.1m\right)^{2}}$$

Multiply 9 and 1000000000 to get 9000000000.

$$\frac{\frac{9000000000Nm^{2}}{c^{2}}\times 1\times 10^{-2}c^{-2}}{\left(3.1m\right)^{2}}$$

Calculate 10 to the power of -2 and get \frac{1}{100}.

$$\frac{\frac{9000000000Nm^{2}}{c^{2}}\times 1\times \frac{1}{100}c^{-2}}{\left(3.1m\right)^{2}}$$

Multiply 1 and \frac{1}{100} to get \frac{1}{100}.

$$\frac{\frac{9000000000Nm^{2}}{c^{2}}\times \frac{1}{100}c^{-2}}{\left(3.1m\right)^{2}}$$

Multiply \frac{9000000000Nm^{2}}{c^{2}} times \frac{1}{100} by multiplying numerator times numerator and denominator times denominator.

$$\frac{\frac{9000000000Nm^{2}}{c^{2}\times 100}c^{-2}}{\left(3.1m\right)^{2}}$$

Cancel out 100 in both numerator and denominator.

$$\frac{\frac{90000000Nm^{2}}{c^{2}}c^{-2}}{\left(3.1m\right)^{2}}$$

Express \frac{90000000Nm^{2}}{c^{2}}c^{-2} as a single fraction.

$$\frac{\frac{90000000Nm^{2}c^{-2}}{c^{2}}}{\left(3.1m\right)^{2}}$$

To divide powers of the same base, subtract the numerator's exponent from the denominator's exponent.

$$\frac{\frac{90000000Nm^{2}}{c^{4}}}{\left(3.1m\right)^{2}}$$

Expand \left(3.1m\right)^{2}.

$$\frac{\frac{90000000Nm^{2}}{c^{4}}}{3.1^{2}m^{2}}$$

Calculate 3.1 to the power of 2 and get 9.61.

$$\frac{\frac{90000000Nm^{2}}{c^{4}}}{9.61m^{2}}$$

Express \frac{\frac{90000000Nm^{2}}{c^{4}}}{9.61m^{2}} as a single fraction.

$$\frac{90000000Nm^{2}}{c^{4}\times 9.61m^{2}}$$

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

$$\frac{90000000N}{9.61c^{4}}$$

Expand

$$\frac{9000000000N}{961c^{4}}$$

Solution Steps

Calculate 10 to the power of 9 and get 1000000000.

$$\frac{\frac{9\times 1000000000Nm^{2}}{c^{2}}\times 1\times 10^{-2}c^{-2}}{\left(3.1m\right)^{2}}$$

Multiply 9 and 1000000000 to get 9000000000.

$$\frac{\frac{9000000000Nm^{2}}{c^{2}}\times 1\times 10^{-2}c^{-2}}{\left(3.1m\right)^{2}}$$

Calculate 10 to the power of -2 and get \frac{1}{100}.

$$\frac{\frac{9000000000Nm^{2}}{c^{2}}\times 1\times \frac{1}{100}c^{-2}}{\left(3.1m\right)^{2}}$$

Multiply 1 and \frac{1}{100} to get \frac{1}{100}.

$$\frac{\frac{9000000000Nm^{2}}{c^{2}}\times \frac{1}{100}c^{-2}}{\left(3.1m\right)^{2}}$$

Multiply \frac{9000000000Nm^{2}}{c^{2}} times \frac{1}{100} by multiplying numerator times numerator and denominator times denominator.

$$\frac{\frac{9000000000Nm^{2}}{c^{2}\times 100}c^{-2}}{\left(3.1m\right)^{2}}$$

Cancel out 100 in both numerator and denominator.

$$\frac{\frac{90000000Nm^{2}}{c^{2}}c^{-2}}{\left(3.1m\right)^{2}}$$

Express \frac{90000000Nm^{2}}{c^{2}}c^{-2} as a single fraction.

$$\frac{\frac{90000000Nm^{2}c^{-2}}{c^{2}}}{\left(3.1m\right)^{2}}$$

To divide powers of the same base, subtract the numerator's exponent from the denominator's exponent.

$$\frac{\frac{90000000Nm^{2}}{c^{4}}}{\left(3.1m\right)^{2}}$$

Expand \left(3.1m\right)^{2}.

$$\frac{\frac{90000000Nm^{2}}{c^{4}}}{3.1^{2}m^{2}}$$

Calculate 3.1 to the power of 2 and get 9.61.

$$\frac{\frac{90000000Nm^{2}}{c^{4}}}{9.61m^{2}}$$

Express \frac{\frac{90000000Nm^{2}}{c^{4}}}{9.61m^{2}} as a single fraction.

$$\frac{90000000Nm^{2}}{c^{4}\times 9.61m^{2}}$$

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

$$\frac{90000000N}{9.61c^{4}}$$