Solve 100*1.6*10^101*5*10^2/9.1*10^-31*10^7

$$\frac { 100 \times 1.6 \times 10 ^ { 101 } \times 5 \times 10 ^ { 2 } } { 9.1 \times 10 ^ { - 31 } \times 10 ^ { 7 } }$$

Evaluate

$$\frac{80000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000}{91}\approx 8.791208791 \cdot 10^{128}$$

Solution Steps

To multiply powers of the same base, add their exponents. Add 101 and 2 to get 103.

$$\frac{100\times 1.6\times 10^{103}\times 5}{9.1\times 10^{-31}\times 10^{7}}$$

To multiply powers of the same base, add their exponents. Add -31 and 7 to get -24.

$$\frac{100\times 1.6\times 10^{103}\times 5}{9.1\times 10^{-24}}$$

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

$$\frac{1.6\times 5\times 100\times 10^{127}}{9.1}$$

Multiply 1.6 and 5 to get 8.

$$\frac{8\times 100\times 10^{127}}{9.1}$$

Multiply 8 and 100 to get 800.

$$\frac{800\times 10^{127}}{9.1}$$

Calculate 10 to the power of 127 and get 10000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000.

$$\frac{800\times 10000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000}{9.1}$$

Multiply 800 and 10000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000 to get 8000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000.

$$\frac{8000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000}{9.1}$$

Expand \frac{8000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000}{9.1} by multiplying both numerator and the denominator by 10.

$$\frac{80000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000}{91}$$

Factor

$$\frac{2 ^ {133} \cdot 5 ^ {130}}{7 \cdot 13} = 8.791208791208792 \times 10^{128}\frac{39}{91} = 8.791208791208792 \times 10^{128}$$