Solve =frac{6*7*10^{-11}Nkg^{2}m^{2}*1.9*10^27kg*1.99*10^10kg}{(7.8*10^10m)^2}

$$= \frac { 6 \cdot 7 \times 10 ^ { - 11 } N kg ^ { 2 } m ^ { 2 } \times 1.9 \times 10 ^ { 27 } kg \times 1.99 \times 10 ^ { 10 } kg } { ( 7.8 \times 10 ^ { 10 } m ) ^ { 2 } }$$

Evaluate

$$\frac{1323350000Nk^{3}g^{4}}{507}$$

Solution Steps

To multiply powers of the same base, add their exponents. Add -11 and 27 to get 16.

$$\frac{6\times 7\times 10^{16}Nkg^{2}m^{2}\times 1.9kg\times 1.99\times 10^{10}kg}{\left(7.8\times 10^{10}m\right)^{2}}$$

To multiply powers of the same base, add their exponents. Add 16 and 10 to get 26.

$$\frac{6\times 7\times 10^{26}Nkg^{2}m^{2}\times 1.9kg\times 1.99kg}{\left(7.8\times 10^{10}m\right)^{2}}$$

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

$$\frac{6\times 7\times 10^{26}Nk^{2}g^{2}m^{2}\times 1.9g\times 1.99kg}{\left(7.8\times 10^{10}m\right)^{2}}$$

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

$$\frac{6\times 7\times 10^{26}Nk^{3}g^{2}m^{2}\times 1.9g\times 1.99g}{\left(7.8\times 10^{10}m\right)^{2}}$$

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

$$\frac{6\times 7\times 10^{26}Nk^{3}g^{3}m^{2}\times 1.9\times 1.99g}{\left(7.8\times 10^{10}m\right)^{2}}$$

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

$$\frac{6\times 7\times 10^{26}Nk^{3}g^{4}m^{2}\times 1.9\times 1.99}{\left(7.8\times 10^{10}m\right)^{2}}$$

Multiply 6 and 7 to get 42.

$$\frac{42\times 10^{26}Nk^{3}g^{4}m^{2}\times 1.9\times 1.99}{\left(7.8\times 10^{10}m\right)^{2}}$$

Calculate 10 to the power of 26 and get 100000000000000000000000000.

$$\frac{42\times 100000000000000000000000000Nk^{3}g^{4}m^{2}\times 1.9\times 1.99}{\left(7.8\times 10^{10}m\right)^{2}}$$

Multiply 42 and 100000000000000000000000000 to get 4200000000000000000000000000.

$$\frac{4200000000000000000000000000Nk^{3}g^{4}m^{2}\times 1.9\times 1.99}{\left(7.8\times 10^{10}m\right)^{2}}$$

Multiply 4200000000000000000000000000 and 1.9 to get 7980000000000000000000000000.

$$\frac{7980000000000000000000000000Nk^{3}g^{4}m^{2}\times 1.99}{\left(7.8\times 10^{10}m\right)^{2}}$$

Multiply 7980000000000000000000000000 and 1.99 to get 15880200000000000000000000000.

$$\frac{15880200000000000000000000000Nk^{3}g^{4}m^{2}}{\left(7.8\times 10^{10}m\right)^{2}}$$

Calculate 10 to the power of 10 and get 10000000000.

$$\frac{15880200000000000000000000000Nk^{3}g^{4}m^{2}}{\left(7.8\times 10000000000m\right)^{2}}$$

Multiply 7.8 and 10000000000 to get 78000000000.

$$\frac{15880200000000000000000000000Nk^{3}g^{4}m^{2}}{\left(78000000000m\right)^{2}}$$

Expand \left(78000000000m\right)^{2}.

$$\frac{15880200000000000000000000000Nk^{3}g^{4}m^{2}}{78000000000^{2}m^{2}}$$

Calculate 78000000000 to the power of 2 and get 6084000000000000000000.

$$\frac{15880200000000000000000000000Nk^{3}g^{4}m^{2}}{6084000000000000000000m^{2}}$$

Cancel out 12000000000000000000m^{2} in both numerator and denominator.

$$\frac{1323350000Nk^{3}g^{4}}{507}$$

Expand

$$\frac{1323350000Nk^{3}g^{4}}{507}$$

Solution Steps

To multiply powers of the same base, add their exponents. Add -11 and 27 to get 16.

$$\frac{6\times 7\times 10^{16}Nkg^{2}m^{2}\times 1.9kg\times 1.99\times 10^{10}kg}{\left(7.8\times 10^{10}m\right)^{2}}$$

To multiply powers of the same base, add their exponents. Add 16 and 10 to get 26.

$$\frac{6\times 7\times 10^{26}Nkg^{2}m^{2}\times 1.9kg\times 1.99kg}{\left(7.8\times 10^{10}m\right)^{2}}$$

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

$$\frac{6\times 7\times 10^{26}Nk^{2}g^{2}m^{2}\times 1.9g\times 1.99kg}{\left(7.8\times 10^{10}m\right)^{2}}$$

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

$$\frac{6\times 7\times 10^{26}Nk^{3}g^{2}m^{2}\times 1.9g\times 1.99g}{\left(7.8\times 10^{10}m\right)^{2}}$$

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

$$\frac{6\times 7\times 10^{26}Nk^{3}g^{3}m^{2}\times 1.9\times 1.99g}{\left(7.8\times 10^{10}m\right)^{2}}$$

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

$$\frac{6\times 7\times 10^{26}Nk^{3}g^{4}m^{2}\times 1.9\times 1.99}{\left(7.8\times 10^{10}m\right)^{2}}$$

Multiply 6 and 7 to get 42.

$$\frac{42\times 10^{26}Nk^{3}g^{4}m^{2}\times 1.9\times 1.99}{\left(7.8\times 10^{10}m\right)^{2}}$$

Calculate 10 to the power of 26 and get 100000000000000000000000000.

$$\frac{42\times 100000000000000000000000000Nk^{3}g^{4}m^{2}\times 1.9\times 1.99}{\left(7.8\times 10^{10}m\right)^{2}}$$

Multiply 42 and 100000000000000000000000000 to get 4200000000000000000000000000.

$$\frac{4200000000000000000000000000Nk^{3}g^{4}m^{2}\times 1.9\times 1.99}{\left(7.8\times 10^{10}m\right)^{2}}$$

Multiply 4200000000000000000000000000 and 1.9 to get 7980000000000000000000000000.

$$\frac{7980000000000000000000000000Nk^{3}g^{4}m^{2}\times 1.99}{\left(7.8\times 10^{10}m\right)^{2}}$$

Multiply 7980000000000000000000000000 and 1.99 to get 15880200000000000000000000000.

$$\frac{15880200000000000000000000000Nk^{3}g^{4}m^{2}}{\left(7.8\times 10^{10}m\right)^{2}}$$

Calculate 10 to the power of 10 and get 10000000000.

$$\frac{15880200000000000000000000000Nk^{3}g^{4}m^{2}}{\left(7.8\times 10000000000m\right)^{2}}$$

Multiply 7.8 and 10000000000 to get 78000000000.

$$\frac{15880200000000000000000000000Nk^{3}g^{4}m^{2}}{\left(78000000000m\right)^{2}}$$

Expand \left(78000000000m\right)^{2}.

$$\frac{15880200000000000000000000000Nk^{3}g^{4}m^{2}}{78000000000^{2}m^{2}}$$

Calculate 78000000000 to the power of 2 and get 6084000000000000000000.

$$\frac{15880200000000000000000000000Nk^{3}g^{4}m^{2}}{6084000000000000000000m^{2}}$$

Cancel out 12000000000000000000m^{2} in both numerator and denominator.

$$\frac{1323350000Nk^{3}g^{4}}{507}$$