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

$$\frac{6052246093750000000000000000000000000000000Nk^{3}g^{4}}{3}$$

Solution Steps

To multiply powers of the same base, add their exponents. Add 11 and 24 to get 35.

$$\frac{6.7\times 10^{35}Nm^{2}kg^{2}\times 6kg\times 7.4\times 10^{22}kg}{\left(3.84\times 10^{8}m\right)^{2}}$$

To multiply powers of the same base, add their exponents. Add 35 and 22 to get 57.

$$\frac{6.7\times 10^{57}Nm^{2}kg^{2}\times 6kg\times 7.4kg}{\left(3.84\times 10^{8}m\right)^{2}}$$

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

$$\frac{6.7\times 10^{57}Nm^{2}k^{2}g^{2}\times 6g\times 7.4kg}{\left(3.84\times 10^{8}m\right)^{2}}$$

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

$$\frac{6.7\times 10^{57}Nm^{2}k^{3}g^{2}\times 6g\times 7.4g}{\left(3.84\times 10^{8}m\right)^{2}}$$

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

$$\frac{6.7\times 10^{57}Nm^{2}k^{3}g^{3}\times 6\times 7.4g}{\left(3.84\times 10^{8}m\right)^{2}}$$

To multiply powers of the same base, add their exponents. Add 3 and 1 to get 4.

$$\frac{6.7\times 10^{57}Nm^{2}k^{3}g^{4}\times 6\times 7.4}{\left(3.84\times 10^{8}m\right)^{2}}$$

Calculate 10 to the power of 57 and get 1000000000000000000000000000000000000000000000000000000000.

$$\frac{6.7\times 1000000000000000000000000000000000000000000000000000000000Nm^{2}k^{3}g^{4}\times 6\times 7.4}{\left(3.84\times 10^{8}m\right)^{2}}$$

Multiply 6.7 and 1000000000000000000000000000000000000000000000000000000000 to get 6700000000000000000000000000000000000000000000000000000000.

$$\frac{6700000000000000000000000000000000000000000000000000000000Nm^{2}k^{3}g^{4}\times 6\times 7.4}{\left(3.84\times 10^{8}m\right)^{2}}$$

Multiply 6700000000000000000000000000000000000000000000000000000000 and 6 to get 40200000000000000000000000000000000000000000000000000000000.

$$\frac{40200000000000000000000000000000000000000000000000000000000Nm^{2}k^{3}g^{4}\times 7.4}{\left(3.84\times 10^{8}m\right)^{2}}$$

Multiply 40200000000000000000000000000000000000000000000000000000000 and 7.4 to get 297480000000000000000000000000000000000000000000000000000000.

$$\frac{297480000000000000000000000000000000000000000000000000000000Nm^{2}k^{3}g^{4}}{\left(3.84\times 10^{8}m\right)^{2}}$$

Calculate 10 to the power of 8 and get 100000000.

$$\frac{297480000000000000000000000000000000000000000000000000000000Nm^{2}k^{3}g^{4}}{\left(3.84\times 100000000m\right)^{2}}$$

Multiply 3.84 and 100000000 to get 384000000.

$$\frac{297480000000000000000000000000000000000000000000000000000000Nm^{2}k^{3}g^{4}}{\left(384000000m\right)^{2}}$$

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

$$\frac{297480000000000000000000000000000000000000000000000000000000Nm^{2}k^{3}g^{4}}{384000000^{2}m^{2}}$$

Calculate 384000000 to the power of 2 and get 147456000000000000.

$$\frac{297480000000000000000000000000000000000000000000000000000000Nm^{2}k^{3}g^{4}}{147456000000000000m^{2}}$$

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

$$\frac{6052246093750000000000000000000000000000000Nk^{3}g^{4}}{3}$$

Expand

$$\frac{6052246093750000000000000000000000000000000Nk^{3}g^{4}}{3}$$

Solution Steps

To multiply powers of the same base, add their exponents. Add 11 and 24 to get 35.

$$\frac{6.7\times 10^{35}Nm^{2}kg^{2}\times 6kg\times 7.4\times 10^{22}kg}{\left(3.84\times 10^{8}m\right)^{2}}$$

To multiply powers of the same base, add their exponents. Add 35 and 22 to get 57.

$$\frac{6.7\times 10^{57}Nm^{2}kg^{2}\times 6kg\times 7.4kg}{\left(3.84\times 10^{8}m\right)^{2}}$$

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

$$\frac{6.7\times 10^{57}Nm^{2}k^{2}g^{2}\times 6g\times 7.4kg}{\left(3.84\times 10^{8}m\right)^{2}}$$

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

$$\frac{6.7\times 10^{57}Nm^{2}k^{3}g^{2}\times 6g\times 7.4g}{\left(3.84\times 10^{8}m\right)^{2}}$$

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

$$\frac{6.7\times 10^{57}Nm^{2}k^{3}g^{3}\times 6\times 7.4g}{\left(3.84\times 10^{8}m\right)^{2}}$$

To multiply powers of the same base, add their exponents. Add 3 and 1 to get 4.

$$\frac{6.7\times 10^{57}Nm^{2}k^{3}g^{4}\times 6\times 7.4}{\left(3.84\times 10^{8}m\right)^{2}}$$

Calculate 10 to the power of 57 and get 1000000000000000000000000000000000000000000000000000000000.

$$\frac{6.7\times 1000000000000000000000000000000000000000000000000000000000Nm^{2}k^{3}g^{4}\times 6\times 7.4}{\left(3.84\times 10^{8}m\right)^{2}}$$

Multiply 6.7 and 1000000000000000000000000000000000000000000000000000000000 to get 6700000000000000000000000000000000000000000000000000000000.

$$\frac{6700000000000000000000000000000000000000000000000000000000Nm^{2}k^{3}g^{4}\times 6\times 7.4}{\left(3.84\times 10^{8}m\right)^{2}}$$

Multiply 6700000000000000000000000000000000000000000000000000000000 and 6 to get 40200000000000000000000000000000000000000000000000000000000.

$$\frac{40200000000000000000000000000000000000000000000000000000000Nm^{2}k^{3}g^{4}\times 7.4}{\left(3.84\times 10^{8}m\right)^{2}}$$

Multiply 40200000000000000000000000000000000000000000000000000000000 and 7.4 to get 297480000000000000000000000000000000000000000000000000000000.

$$\frac{297480000000000000000000000000000000000000000000000000000000Nm^{2}k^{3}g^{4}}{\left(3.84\times 10^{8}m\right)^{2}}$$

Calculate 10 to the power of 8 and get 100000000.

$$\frac{297480000000000000000000000000000000000000000000000000000000Nm^{2}k^{3}g^{4}}{\left(3.84\times 100000000m\right)^{2}}$$

Multiply 3.84 and 100000000 to get 384000000.

$$\frac{297480000000000000000000000000000000000000000000000000000000Nm^{2}k^{3}g^{4}}{\left(384000000m\right)^{2}}$$

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

$$\frac{297480000000000000000000000000000000000000000000000000000000Nm^{2}k^{3}g^{4}}{384000000^{2}m^{2}}$$

Calculate 384000000 to the power of 2 and get 147456000000000000.

$$\frac{297480000000000000000000000000000000000000000000000000000000Nm^{2}k^{3}g^{4}}{147456000000000000m^{2}}$$

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

$$\frac{6052246093750000000000000000000000000000000Nk^{3}g^{4}}{3}$$