Solve 31^-9+210^-10/7.910^-20+1010^-21

$$\frac{ 3 { 1 }^{ -9 } +2 { 10 }^{ -10 } }{ 7.9 { 10 }^{ -20 } +10 { 10 }^{ -21 } }$$

Evaluate

$$\frac{3000000000200000000000}{89}\approx 3.370786517 \cdot 10^{19}$$

Solution Steps

To multiply powers of the same base, add their exponents. Add 1 and -21 to get -20.

$$\frac{3\times 1^{-9}+2\times 10^{-10}}{7.9\times 10^{-20}+10^{-20}}$$

Calculate 1 to the power of -9 and get 1.

$$\frac{3\times 1+2\times 10^{-10}}{7.9\times 10^{-20}+10^{-20}}$$

Multiply 3 and 1 to get 3.

$$\frac{3+2\times 10^{-10}}{7.9\times 10^{-20}+10^{-20}}$$

Calculate 10 to the power of -10 and get \frac{1}{10000000000}.

$$\frac{3+2\times \frac{1}{10000000000}}{7.9\times 10^{-20}+10^{-20}}$$

Multiply 2 and \frac{1}{10000000000} to get \frac{1}{5000000000}.

$$\frac{3+\frac{1}{5000000000}}{7.9\times 10^{-20}+10^{-20}}$$

Add 3 and \frac{1}{5000000000} to get \frac{15000000001}{5000000000}.

$$\frac{\frac{15000000001}{5000000000}}{7.9\times 10^{-20}+10^{-20}}$$

Calculate 10 to the power of -20 and get \frac{1}{100000000000000000000}.

$$\frac{\frac{15000000001}{5000000000}}{7.9\times \frac{1}{100000000000000000000}+10^{-20}}$$

Multiply 7.9 and \frac{1}{100000000000000000000} to get \frac{79}{1000000000000000000000}.

$$\frac{\frac{15000000001}{5000000000}}{\frac{79}{1000000000000000000000}+10^{-20}}$$

Calculate 10 to the power of -20 and get \frac{1}{100000000000000000000}.

$$\frac{\frac{15000000001}{5000000000}}{\frac{79}{1000000000000000000000}+\frac{1}{100000000000000000000}}$$

Add \frac{79}{1000000000000000000000} and \frac{1}{100000000000000000000} to get \frac{89}{1000000000000000000000}.

$$\frac{\frac{15000000001}{5000000000}}{\frac{89}{1000000000000000000000}}$$

Divide \frac{15000000001}{5000000000} by \frac{89}{1000000000000000000000} by multiplying \frac{15000000001}{5000000000} by the reciprocal of \frac{89}{1000000000000000000000}.

$$\frac{15000000001}{5000000000}\times \frac{1000000000000000000000}{89}$$

Multiply \frac{15000000001}{5000000000} and \frac{1000000000000000000000}{89} to get \frac{3000000000200000000000}{89}.

$$\frac{3000000000200000000000}{89}$$

Factor

$$\frac{306122449 \cdot 2 ^ {12} \cdot 5 ^ {11} \cdot 7 ^ {2}}{89} = 3.3707865170786513 \times 10^{19}\frac{75}{89} = 3.3707865170786513 \times 10^{19}$$