Solve 3.47*10^22div6.67*10^-11div6*10^24*1.5*10^11*1.5*{10}^11

$$3.47 \times { 10 }^{ 22 } \div 6.67 \times { 10 }^{ -11 } \div 6 \times { 10 }^{ 24 } \times 1.5 \times { 10 }^{ 11 } \times 1.5 \times { 10 }^{ 11 }$$

Evaluate

$$\frac{130125000000000000000000000000000000000000000000000000000000}{667}\approx 1.95089955 \cdot 10^{56}$$

Solution Steps

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

$$\frac{\frac{3.47\times 10^{22}}{6.67}\times 10^{-11}}{6}\times 10^{35}\times 1.5\times 1.5\times 10^{11}$$

To multiply powers of the same base, add their exponents. Add 35 and 11 to get 46.

$$\frac{\frac{3.47\times 10^{22}}{6.67}\times 10^{-11}}{6}\times 10^{46}\times 1.5\times 1.5$$

Calculate 10 to the power of 22 and get 10000000000000000000000.

$$\frac{\frac{3.47\times 10000000000000000000000}{6.67}\times 10^{-11}}{6}\times 10^{46}\times 1.5\times 1.5$$

Multiply 3.47 and 10000000000000000000000 to get 34700000000000000000000.

$$\frac{\frac{34700000000000000000000}{6.67}\times 10^{-11}}{6}\times 10^{46}\times 1.5\times 1.5$$

Expand \frac{34700000000000000000000}{6.67} by multiplying both numerator and the denominator by 100.

$$\frac{\frac{3470000000000000000000000}{667}\times 10^{-11}}{6}\times 10^{46}\times 1.5\times 1.5$$

Calculate 10 to the power of -11 and get \frac{1}{100000000000}.

$$\frac{\frac{3470000000000000000000000}{667}\times \frac{1}{100000000000}}{6}\times 10^{46}\times 1.5\times 1.5$$

Multiply \frac{3470000000000000000000000}{667} and \frac{1}{100000000000} to get \frac{34700000000000}{667}.

$$\frac{\frac{34700000000000}{667}}{6}\times 10^{46}\times 1.5\times 1.5$$

Express \frac{\frac{34700000000000}{667}}{6} as a single fraction.

$$\frac{34700000000000}{667\times 6}\times 10^{46}\times 1.5\times 1.5$$

Multiply 667 and 6 to get 4002.

$$\frac{34700000000000}{4002}\times 10^{46}\times 1.5\times 1.5$$

Reduce the fraction \frac{34700000000000}{4002} to lowest terms by extracting and canceling out 2.

$$\frac{17350000000000}{2001}\times 10^{46}\times 1.5\times 1.5$$

Calculate 10 to the power of 46 and get 10000000000000000000000000000000000000000000000.

$$\frac{17350000000000}{2001}\times 10000000000000000000000000000000000000000000000\times 1.5\times 1.5$$

Multiply \frac{17350000000000}{2001} and 10000000000000000000000000000000000000000000000 to get \frac{173500000000000000000000000000000000000000000000000000000000}{2001}.

$$\frac{173500000000000000000000000000000000000000000000000000000000}{2001}\times 1.5\times 1.5$$

Multiply \frac{173500000000000000000000000000000000000000000000000000000000}{2001} and 1.5 to get \frac{86750000000000000000000000000000000000000000000000000000000}{667}.

$$\frac{86750000000000000000000000000000000000000000000000000000000}{667}\times 1.5$$

Multiply \frac{86750000000000000000000000000000000000000000000000000000000}{667} and 1.5 to get \frac{130125000000000000000000000000000000000000000000000000000000}{667}.

$$\frac{130125000000000000000000000000000000000000000000000000000000}{667}$$

Factor

$$\frac{3 \cdot 347 \cdot 2 ^ {54} \cdot 5 ^ {57}}{23 \cdot 29} = 1.9508995502248876 \times 10^{56}\frac{366}{667} = 1.9508995502248876 \times 10^{56}$$