Solve 6,63*10^-34*3*10^8/0,42*10^-6-1,6*10^-19*0,75

$$\frac { 6,63 \cdot 10 ^ { - 34 } \cdot 3 \cdot 10 ^ { 8 } } { 0,42 \cdot 10 ^ { - 6 } } - 1,6 \cdot 10 ^ { - 19 } \cdot 0,75$$

Evaluate

$$\frac{99}{280000000000000000000}\approx 3,535714286 \cdot 10^{-19}$$

Solution Steps

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

$$\frac{6,63\times 10^{-26}\times 3}{0,42\times 10^{-6}}-1,6\times 10^{-19}\times 0,75$$

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

$$\frac{3\times 6,63}{0,42\times 10^{20}}-1,6\times 10^{-19}\times 0,75$$

Multiply 3 and 6,63 to get 19,89.

$$\frac{19,89}{0,42\times 10^{20}}-1,6\times 10^{-19}\times 0,75$$

Calculate 10 to the power of 20 and get 100000000000000000000.

$$\frac{19,89}{0,42\times 100000000000000000000}-1,6\times 10^{-19}\times 0,75$$

Multiply 0,42 and 100000000000000000000 to get 42000000000000000000.

$$\frac{19,89}{42000000000000000000}-1,6\times 10^{-19}\times 0,75$$

Expand \frac{19,89}{42000000000000000000} by multiplying both numerator and the denominator by 100.

$$\frac{1989}{4200000000000000000000}-1,6\times 10^{-19}\times 0,75$$

Reduce the fraction \frac{1989}{4200000000000000000000} to lowest terms by extracting and canceling out 3.

$$\frac{663}{1400000000000000000000}-1,6\times 10^{-19}\times 0,75$$

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

$$\frac{663}{1400000000000000000000}-1,6\times \frac{1}{10000000000000000000}\times 0,75$$

Multiply 1,6 and \frac{1}{10000000000000000000} to get \frac{1}{6250000000000000000}.

$$\frac{663}{1400000000000000000000}-\frac{1}{6250000000000000000}\times 0,75$$

Multiply \frac{1}{6250000000000000000} and 0,75 to get \frac{3}{25000000000000000000}.

$$\frac{663}{1400000000000000000000}-\frac{3}{25000000000000000000}$$

Subtract \frac{3}{25000000000000000000} from \frac{663}{1400000000000000000000} to get \frac{99}{280000000000000000000}.

$$\frac{99}{280000000000000000000}$$

Factor

$$\frac{11 \cdot 3 ^ {2}}{7 \cdot 2 ^ {21} \cdot 5 ^ {19}} = 3.5357142857142856 \times 10^{-19}$$