Solve 6.63*10^-34*3*10^8/5.15*1.6^-19

$$\frac{ 6.63 \times { 10 }^{ -34 } \times 3 \times { 10 }^{ 8 } }{ 5.15 \times { 1.6 }^{ -19 } }$$

Evaluate

$$\frac{4271344975872}{14637180356658063828945159912109375}\approx 2.918147397 \cdot 10^{-22}$$

Solution Steps

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

$$\frac{6.63\times 10^{-26}\times 3}{5.15\times 1.6^{-19}}$$

Calculate 10 to the power of -26 and get \frac{1}{100000000000000000000000000}.

$$\frac{6.63\times \frac{1}{100000000000000000000000000}\times 3}{5.15\times 1.6^{-19}}$$

Multiply 6.63 and \frac{1}{100000000000000000000000000} to get \frac{663}{10000000000000000000000000000}.

$$\frac{\frac{663}{10000000000000000000000000000}\times 3}{5.15\times 1.6^{-19}}$$

Multiply \frac{663}{10000000000000000000000000000} and 3 to get \frac{1989}{10000000000000000000000000000}.

$$\frac{\frac{1989}{10000000000000000000000000000}}{5.15\times 1.6^{-19}}$$

Calculate 1.6 to the power of -19 and get 0.000132348898008484427979425390731194056570529937744140625.

$$\frac{\frac{1989}{10000000000000000000000000000}}{5.15\times 0.000132348898008484427979425390731194056570529937744140625}$$

Multiply 5.15 and 0.000132348898008484427979425390731194056570529937744140625 to get 0.00068159682474369480409404076226564939133822917938232421875.

$$\frac{\frac{1989}{10000000000000000000000000000}}{0.00068159682474369480409404076226564939133822917938232421875}$$

Express \frac{\frac{1989}{10000000000000000000000000000}}{0.00068159682474369480409404076226564939133822917938232421875} as a single fraction.

$$\frac{1989}{10000000000000000000000000000\times 0.00068159682474369480409404076226564939133822917938232421875}$$

Multiply 10000000000000000000000000000 and 0.00068159682474369480409404076226564939133822917938232421875 to get 6815968247436948040940407.6226564939133822917938232421875.

$$\frac{1989}{6815968247436948040940407.6226564939133822917938232421875}$$

Expand \frac{1989}{6815968247436948040940407.6226564939133822917938232421875} by multiplying both numerator and the denominator by 10000000000000000000000000000000.

$$\frac{19890000000000000000000000000000000}{68159682474369480409404076226564939133822917938232421875}$$

Reduce the fraction \frac{19890000000000000000000000000000000}{68159682474369480409404076226564939133822917938232421875} to lowest terms by extracting and canceling out 4656612873077392578125.

$$\frac{4271344975872}{14637180356658063828945159912109375}$$

Factor

$$\frac{13 \cdot 17 \cdot 2 ^ {31} \cdot 3 ^ {2}}{103 \cdot 5 ^ {46}} = 2.918147397103759 \times 10^{-22}$$