Solve 6.6*10^-34*3*10^8/6.6*10^-34*3*10^8/290*{10^-9}+1.5*1.6*{10}^-19

$$\frac{ \frac{ 6.6 \times { 10 }^{ -34 } \times 3 \times { 10 }^{ 8 } }{ 6.6 \times { 10 }^{ -34 } \times 3 \times { 10 }^{ 8 } } }{ 290 \times { 10 }^{ -9 } } +1.5 \times 1.6 \times { 10 }^{ -19 }$$

Evaluate

$$\frac{1250000000000000000000000087}{362500000000000000000}\approx 3448275.862068966$$

Solution Steps

To multiply powers of the same base, add their exponents. Add -34 and 8 to get -26.

$$\frac{\frac{6.6\times 10^{-26}\times 3}{6.6\times 10^{-34}\times 3\times 10^{8}}}{290\times 10^{-9}}+1.5\times 1.6\times 10^{-19}$$

To multiply powers of the same base, add their exponents. Add -34 and 8 to get -26.

$$\frac{\frac{6.6\times 10^{-26}\times 3}{6.6\times 10^{-26}\times 3}}{290\times 10^{-9}}+1.5\times 1.6\times 10^{-19}$$

Divide 6.6\times 10^{-26}\times 3 by 6.6\times 10^{-26}\times 3 to get 1.

$$\frac{1}{290\times 10^{-9}}+1.5\times 1.6\times 10^{-19}$$

Calculate 10 to the power of -9 and get \frac{1}{1000000000}.

$$\frac{1}{290\times \frac{1}{1000000000}}+1.5\times 1.6\times 10^{-19}$$

Multiply 290 and \frac{1}{1000000000} to get \frac{29}{100000000}.

$$\frac{1}{\frac{29}{100000000}}+1.5\times 1.6\times 10^{-19}$$

Divide 1 by \frac{29}{100000000} by multiplying 1 by the reciprocal of \frac{29}{100000000}.

$$1\times \frac{100000000}{29}+1.5\times 1.6\times 10^{-19}$$

Multiply 1 and \frac{100000000}{29} to get \frac{100000000}{29}.

$$\frac{100000000}{29}+1.5\times 1.6\times 10^{-19}$$

Multiply 1.5 and 1.6 to get 2.4.

$$\frac{100000000}{29}+2.4\times 10^{-19}$$

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

$$\frac{100000000}{29}+2.4\times \frac{1}{10000000000000000000}$$

Multiply 2.4 and \frac{1}{10000000000000000000} to get \frac{3}{12500000000000000000}.

$$\frac{100000000}{29}+\frac{3}{12500000000000000000}$$

Add \frac{100000000}{29} and \frac{3}{12500000000000000000} to get \frac{1250000000000000000000000087}{362500000000000000000}.

$$\frac{1250000000000000000000000087}{362500000000000000000}$$

Factor

$$\frac{7 \cdot 83 \cdot 173 \cdot 12436202282291842846199}{29 \cdot 2 ^ {17} \cdot 5 ^ {20}} = 3448275\frac{3.1249999994788995 \times 10^{20}}{3.625 \times 10^{20}} \approx 3448275.862068966$$