Solve 6.625*10^-34*3*8^10/425*10^-4*1.6*10^-19-1.96

$$\frac{ 6.625 \times { 10 }^{ -34 } \times 3 \times { 8 }^{ 10 } }{ 425 \times { 10 }^{ -4 } \times 1.6 \times { 10 }^{ -19 } } -1.96$$

Evaluate

$$-\frac{8133463097}{4150390625}\approx -1.959686167$$

Solution Steps

To multiply powers of the same base, add their exponents. Add -4 and -19 to get -23.

$$\frac{6.625\times 10^{-34}\times 3\times 8^{10}}{425\times 10^{-23}\times 1.6}-1.96$$

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

$$\frac{3\times 6.625\times 8^{10}}{1.6\times 425\times 10^{11}}-1.96$$

Multiply 3 and 6.625 to get 19.875.

$$\frac{19.875\times 8^{10}}{1.6\times 425\times 10^{11}}-1.96$$

Calculate 8 to the power of 10 and get 1073741824.

$$\frac{19.875\times 1073741824}{1.6\times 425\times 10^{11}}-1.96$$

Multiply 19.875 and 1073741824 to get 21340618752.

$$\frac{21340618752}{1.6\times 425\times 10^{11}}-1.96$$

Multiply 1.6 and 425 to get 680.

$$\frac{21340618752}{680\times 10^{11}}-1.96$$

Calculate 10 to the power of 11 and get 100000000000.

$$\frac{21340618752}{680\times 100000000000}-1.96$$

Multiply 680 and 100000000000 to get 68000000000000.

$$\frac{21340618752}{68000000000000}-1.96$$

Reduce the fraction \frac{21340618752}{68000000000000} to lowest terms by extracting and canceling out 16384.

$$\frac{1302528}{4150390625}-1.96$$

Subtract 1.96 from \frac{1302528}{4150390625} to get -\frac{8133463097}{4150390625}.

$$-\frac{8133463097}{4150390625}$$

Factor

$$-\frac{8133463097}{4150390625} = -1\frac{3983072472}{4150390625} = -1.9596861673712942$$