Solve 5*10^5*(6.4*10^6)/(6.67*10^-11)(6.4*10^24)

$$\frac { 5 \times 10 ^ { 5 } \times ( 6.4 \times 10 ^ { 6 } ) } { ( 6.67 \times 10 ^ { - 11 } ) ( 6.4 \times 10 ^ { 24 } ) }$$

Evaluate

$$\frac{5}{667}\approx 0.007496252$$

Solution Steps

To multiply powers of the same base, add their exponents. Add 5 and 6 to get 11.

$$\frac{5\times 10^{11}\times 6.4}{6.67\times 10^{-11}\times 6.4\times 10^{24}}$$

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

$$\frac{5\times 10^{11}\times 6.4}{6.67\times 10^{13}\times 6.4}$$

Cancel out 10^{11} in both numerator and denominator.

$$\frac{5\times 6.4}{6.4\times 6.67\times 10^{2}}$$

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

$$\frac{5}{6.67\times 6.4^{0}\times 10^{2}}$$

Calculate 6.4 to the power of 0 and get 1.

$$\frac{5}{6.67\times 1\times 10^{2}}$$

Multiply 6.67 and 1 to get 6.67.

$$\frac{5}{6.67\times 10^{2}}$$

Calculate 10 to the power of 2 and get 100.

$$\frac{5}{6.67\times 100}$$

Multiply 6.67 and 100 to get 667.

$$\frac{5}{667}$$

Factor

$$\frac{5}{23 \cdot 29} = 0.0074962518740629685$$