Solve 316*9*10^9left(1.6*10^-19right)^2/6.64*10^-27{left(5*{10^7right)}^-2}

$$\frac{ 316 \cdot 9 \times { 10 }^{ 9 } { \left(1.6 \times { 10 }^{ -19 } \right) }^{ 2 } }{ 6.64 \times { 10 }^{ -27 } { \left(5 \times { 10 }^{ 7 } \right) }^{ -2 } }$$

Evaluate

$$\frac{2275200000000000000}{83}\approx 2.741204819 \cdot 10^{16}$$

Solution Steps

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

$$\frac{9\times 316\times 10^{36}\times \left(1.6\times 10^{-19}\right)^{2}}{6.64\times \left(5\times 10^{7}\right)^{-2}}$$

Multiply 9 and 316 to get 2844.

$$\frac{2844\times 10^{36}\times \left(1.6\times 10^{-19}\right)^{2}}{6.64\times \left(5\times 10^{7}\right)^{-2}}$$

Calculate 10 to the power of 36 and get 1000000000000000000000000000000000000.

$$\frac{2844\times 1000000000000000000000000000000000000\times \left(1.6\times 10^{-19}\right)^{2}}{6.64\times \left(5\times 10^{7}\right)^{-2}}$$

Multiply 2844 and 1000000000000000000000000000000000000 to get 2844000000000000000000000000000000000000.

$$\frac{2844000000000000000000000000000000000000\times \left(1.6\times 10^{-19}\right)^{2}}{6.64\times \left(5\times 10^{7}\right)^{-2}}$$

Calculate 10 to the power of -19 and get \frac{1}{10000000000000000000}.

$$\frac{2844000000000000000000000000000000000000\times \left(1.6\times \frac{1}{10000000000000000000}\right)^{2}}{6.64\times \left(5\times 10^{7}\right)^{-2}}$$

Multiply 1.6 and \frac{1}{10000000000000000000} to get \frac{1}{6250000000000000000}.

$$\frac{2844000000000000000000000000000000000000\times \left(\frac{1}{6250000000000000000}\right)^{2}}{6.64\times \left(5\times 10^{7}\right)^{-2}}$$

Calculate \frac{1}{6250000000000000000} to the power of 2 and get \frac{1}{39062500000000000000000000000000000000}.

$$\frac{2844000000000000000000000000000000000000\times \frac{1}{39062500000000000000000000000000000000}}{6.64\times \left(5\times 10^{7}\right)^{-2}}$$

Multiply 2844000000000000000000000000000000000000 and \frac{1}{39062500000000000000000000000000000000} to get \frac{45504}{625}.

$$\frac{\frac{45504}{625}}{6.64\times \left(5\times 10^{7}\right)^{-2}}$$

Calculate 10 to the power of 7 and get 10000000.

$$\frac{\frac{45504}{625}}{6.64\times \left(5\times 10000000\right)^{-2}}$$

Multiply 5 and 10000000 to get 50000000.

$$\frac{\frac{45504}{625}}{6.64\times 50000000^{-2}}$$

Calculate 50000000 to the power of -2 and get \frac{1}{2500000000000000}.

$$\frac{\frac{45504}{625}}{6.64\times \frac{1}{2500000000000000}}$$

Multiply 6.64 and \frac{1}{2500000000000000} to get \frac{83}{31250000000000000}.

$$\frac{\frac{45504}{625}}{\frac{83}{31250000000000000}}$$

Divide \frac{45504}{625} by \frac{83}{31250000000000000} by multiplying \frac{45504}{625} by the reciprocal of \frac{83}{31250000000000000}.

$$\frac{45504}{625}\times \frac{31250000000000000}{83}$$

Multiply \frac{45504}{625} and \frac{31250000000000000}{83} to get \frac{2275200000000000000}{83}.

$$\frac{2275200000000000000}{83}$$

Factor

$$\frac{79 \cdot 2 ^ {19} \cdot 3 ^ {2} \cdot 5 ^ {14}}{83} = 27412048192771084\frac{28}{83} = 27412048192771084$$