Solve -2/2110^21-1/610^6+1/310/

$$- \frac{ 2 }{ 21 } { 10 }^{ 21 } - \frac{ 1 }{ 6 } { 10 }^{ 6 } + \frac{ 1 }{ 3 } \frac{ 10 }{ }$$

Evaluate

$$-\frac{666666666666667833310}{7}\approx -9.523809524 \cdot 10^{19}$$

Solution Steps

Calculate 10 to the power of 21 and get 1000000000000000000000.

$$-\frac{2}{21}\times 1000000000000000000000-\frac{1}{6}\times 10^{6}+\frac{1}{3}\times \frac{10}{1}$$

Express -\frac{2}{21}\times 1000000000000000000000 as a single fraction.

$$\frac{-2\times 1000000000000000000000}{21}-\frac{1}{6}\times 10^{6}+\frac{1}{3}\times \frac{10}{1}$$

Multiply -2 and 1000000000000000000000 to get -2000000000000000000000.

$$\frac{-2000000000000000000000}{21}-\frac{1}{6}\times 10^{6}+\frac{1}{3}\times \frac{10}{1}$$

Fraction \frac{-2000000000000000000000}{21} can be rewritten as -\frac{2000000000000000000000}{21} by extracting the negative sign.

$$-\frac{2000000000000000000000}{21}-\frac{1}{6}\times 10^{6}+\frac{1}{3}\times \frac{10}{1}$$

Calculate 10 to the power of 6 and get 1000000.

$$-\frac{2000000000000000000000}{21}-\frac{1}{6}\times 1000000+\frac{1}{3}\times \frac{10}{1}$$

Multiply \frac{1}{6} and 1000000 to get \frac{1000000}{6}.

$$-\frac{2000000000000000000000}{21}-\frac{1000000}{6}+\frac{1}{3}\times \frac{10}{1}$$

Reduce the fraction \frac{1000000}{6} to lowest terms by extracting and canceling out 2.

$$-\frac{2000000000000000000000}{21}-\frac{500000}{3}+\frac{1}{3}\times \frac{10}{1}$$

Least common multiple of 21 and 3 is 21. Convert -\frac{2000000000000000000000}{21} and \frac{500000}{3} to fractions with denominator 21.

$$-\frac{2000000000000000000000}{21}-\frac{3500000}{21}+\frac{1}{3}\times \frac{10}{1}$$

Since -\frac{2000000000000000000000}{21} and \frac{3500000}{21} have the same denominator, subtract them by subtracting their numerators.

$$\frac{-2000000000000000000000-3500000}{21}+\frac{1}{3}\times \frac{10}{1}$$

Subtract 3500000 from -2000000000000000000000 to get -2000000000000003500000.

$$-\frac{2000000000000003500000}{21}+\frac{1}{3}\times \frac{10}{1}$$

Anything divided by one gives itself.

$$-\frac{2000000000000003500000}{21}+\frac{1}{3}\times 10$$

Multiply \frac{1}{3} and 10 to get \frac{10}{3}.

$$-\frac{2000000000000003500000}{21}+\frac{10}{3}$$

Least common multiple of 21 and 3 is 21. Convert -\frac{2000000000000003500000}{21} and \frac{10}{3} to fractions with denominator 21.

$$-\frac{2000000000000003500000}{21}+\frac{70}{21}$$

Since -\frac{2000000000000003500000}{21} and \frac{70}{21} have the same denominator, add them by adding their numerators.

$$\frac{-2000000000000003500000+70}{21}$$

Add -2000000000000003500000 and 70 to get -2000000000000003499930.

$$\frac{-2000000000000003499930}{21}$$

Reduce the fraction \frac{-2000000000000003499930}{21} to lowest terms by extracting and canceling out 3.

$$-\frac{666666666666667833310}{7}$$

Factor

$$-\frac{666666666666667833310}{7} = -9.52380952380954 \times 10^{19}\frac{6}{7} = -9.52380952380954 \times 10^{19}$$