Solve =frac{6.7*10^{-11}Nm^{2}kg^{-2}*6*10^24kg*7.4*10^22kg}{(3.84*10^8m)^2}

$$= \frac { 6.7 \times 10 ^ { - 11 } Nm ^ { 2 } kg ^ { - 2 } \times 6 \times 10 ^ { 24 } kg \times 7.4 \times 10 ^ { 22 } kg } { ( 3.84 \times 10 ^ { 8 } m ) ^ { 2 } }$$

Evaluate

$$\frac{605224609375000000000Nk^{3}}{3}$$

Solution Steps

To multiply powers of the same base, add their exponents. Add -11 and 24 to get 13.

$$\frac{6.7\times 10^{13}Nm^{2}kg^{-2}\times 6kg\times 7.4\times 10^{22}kg}{\left(3.84\times 10^{8}m\right)^{2}}$$

To multiply powers of the same base, add their exponents. Add 13 and 22 to get 35.

$$\frac{6.7\times 10^{35}Nm^{2}kg^{-2}\times 6kg\times 7.4kg}{\left(3.84\times 10^{8}m\right)^{2}}$$

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

$$\frac{6.7\times 10^{35}Nm^{2}k^{2}g^{-2}\times 6g\times 7.4kg}{\left(3.84\times 10^{8}m\right)^{2}}$$

To multiply powers of the same base, add their exponents. Add 2 and 1 to get 3.

$$\frac{6.7\times 10^{35}Nm^{2}k^{3}g^{-2}\times 6g\times 7.4g}{\left(3.84\times 10^{8}m\right)^{2}}$$

To multiply powers of the same base, add their exponents. Add -2 and 1 to get -1.

$$\frac{6.7\times 10^{35}Nm^{2}k^{3}g^{-1}\times 6\times 7.4g}{\left(3.84\times 10^{8}m\right)^{2}}$$

Multiply g^{-1} and g to get 1.

$$\frac{6.7\times 10^{35}Nm^{2}k^{3}\times 6\times 7.4}{\left(3.84\times 10^{8}m\right)^{2}}$$

Calculate 10 to the power of 35 and get 100000000000000000000000000000000000.

$$\frac{6.7\times 100000000000000000000000000000000000Nm^{2}k^{3}\times 6\times 7.4}{\left(3.84\times 10^{8}m\right)^{2}}$$

Multiply 6.7 and 100000000000000000000000000000000000 to get 670000000000000000000000000000000000.

$$\frac{670000000000000000000000000000000000Nm^{2}k^{3}\times 6\times 7.4}{\left(3.84\times 10^{8}m\right)^{2}}$$

Multiply 670000000000000000000000000000000000 and 6 to get 4020000000000000000000000000000000000.

$$\frac{4020000000000000000000000000000000000Nm^{2}k^{3}\times 7.4}{\left(3.84\times 10^{8}m\right)^{2}}$$

Multiply 4020000000000000000000000000000000000 and 7.4 to get 29748000000000000000000000000000000000.

$$\frac{29748000000000000000000000000000000000Nm^{2}k^{3}}{\left(3.84\times 10^{8}m\right)^{2}}$$

Calculate 10 to the power of 8 and get 100000000.

$$\frac{29748000000000000000000000000000000000Nm^{2}k^{3}}{\left(3.84\times 100000000m\right)^{2}}$$

Multiply 3.84 and 100000000 to get 384000000.

$$\frac{29748000000000000000000000000000000000Nm^{2}k^{3}}{\left(384000000m\right)^{2}}$$

Expand \left(384000000m\right)^{2}.

$$\frac{29748000000000000000000000000000000000Nm^{2}k^{3}}{384000000^{2}m^{2}}$$

Calculate 384000000 to the power of 2 and get 147456000000000000.

$$\frac{29748000000000000000000000000000000000Nm^{2}k^{3}}{147456000000000000m^{2}}$$

Cancel out 49152000000000000m^{2} in both numerator and denominator.

$$\frac{605224609375000000000Nk^{3}}{3}$$

Expand

$$\frac{605224609375000000000Nk^{3}}{3}$$

Solution Steps

To multiply powers of the same base, add their exponents. Add -11 and 24 to get 13.

$$\frac{6.7\times 10^{13}Nm^{2}kg^{-2}\times 6kg\times 7.4\times 10^{22}kg}{\left(3.84\times 10^{8}m\right)^{2}}$$

To multiply powers of the same base, add their exponents. Add 13 and 22 to get 35.

$$\frac{6.7\times 10^{35}Nm^{2}kg^{-2}\times 6kg\times 7.4kg}{\left(3.84\times 10^{8}m\right)^{2}}$$

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

$$\frac{6.7\times 10^{35}Nm^{2}k^{2}g^{-2}\times 6g\times 7.4kg}{\left(3.84\times 10^{8}m\right)^{2}}$$

To multiply powers of the same base, add their exponents. Add 2 and 1 to get 3.

$$\frac{6.7\times 10^{35}Nm^{2}k^{3}g^{-2}\times 6g\times 7.4g}{\left(3.84\times 10^{8}m\right)^{2}}$$

To multiply powers of the same base, add their exponents. Add -2 and 1 to get -1.

$$\frac{6.7\times 10^{35}Nm^{2}k^{3}g^{-1}\times 6\times 7.4g}{\left(3.84\times 10^{8}m\right)^{2}}$$

Multiply g^{-1} and g to get 1.

$$\frac{6.7\times 10^{35}Nm^{2}k^{3}\times 6\times 7.4}{\left(3.84\times 10^{8}m\right)^{2}}$$

Calculate 10 to the power of 35 and get 100000000000000000000000000000000000.

$$\frac{6.7\times 100000000000000000000000000000000000Nm^{2}k^{3}\times 6\times 7.4}{\left(3.84\times 10^{8}m\right)^{2}}$$

Multiply 6.7 and 100000000000000000000000000000000000 to get 670000000000000000000000000000000000.

$$\frac{670000000000000000000000000000000000Nm^{2}k^{3}\times 6\times 7.4}{\left(3.84\times 10^{8}m\right)^{2}}$$

Multiply 670000000000000000000000000000000000 and 6 to get 4020000000000000000000000000000000000.

$$\frac{4020000000000000000000000000000000000Nm^{2}k^{3}\times 7.4}{\left(3.84\times 10^{8}m\right)^{2}}$$

Multiply 4020000000000000000000000000000000000 and 7.4 to get 29748000000000000000000000000000000000.

$$\frac{29748000000000000000000000000000000000Nm^{2}k^{3}}{\left(3.84\times 10^{8}m\right)^{2}}$$

Calculate 10 to the power of 8 and get 100000000.

$$\frac{29748000000000000000000000000000000000Nm^{2}k^{3}}{\left(3.84\times 100000000m\right)^{2}}$$

Multiply 3.84 and 100000000 to get 384000000.

$$\frac{29748000000000000000000000000000000000Nm^{2}k^{3}}{\left(384000000m\right)^{2}}$$

Expand \left(384000000m\right)^{2}.

$$\frac{29748000000000000000000000000000000000Nm^{2}k^{3}}{384000000^{2}m^{2}}$$

Calculate 384000000 to the power of 2 and get 147456000000000000.

$$\frac{29748000000000000000000000000000000000Nm^{2}k^{3}}{147456000000000000m^{2}}$$

Cancel out 49152000000000000m^{2} in both numerator and denominator.

$$\frac{605224609375000000000Nk^{3}}{3}$$