Solve 2/3-2^33^24-5-2^23^3{4}^2+10

$$\frac{ 2 }{ 3 } - { 2 }^{ 3 } { 3 }^{ 2 } 4-5- { 2 }^{ 2 } { 3 }^{ 3 } { 4 }^{ 2 } +10$$

Evaluate

$$-\frac{6031}{3}\approx -2010.333333333$$

Solution Steps

Calculate 2 to the power of 3 and get 8.

$$\frac{2}{3}-8\times 3^{2}\times 4-5-2^{2}\times 3^{3}\times 4^{2}+10$$

Calculate 3 to the power of 2 and get 9.

$$\frac{2}{3}-8\times 9\times 4-5-2^{2}\times 3^{3}\times 4^{2}+10$$

Multiply 8 and 9 to get 72.

$$\frac{2}{3}-72\times 4-5-2^{2}\times 3^{3}\times 4^{2}+10$$

Multiply 72 and 4 to get 288.

$$\frac{2}{3}-288-5-2^{2}\times 3^{3}\times 4^{2}+10$$

Convert 288 to fraction \frac{864}{3}.

$$\frac{2}{3}-\frac{864}{3}-5-2^{2}\times 3^{3}\times 4^{2}+10$$

Since \frac{2}{3} and \frac{864}{3} have the same denominator, subtract them by subtracting their numerators.

$$\frac{2-864}{3}-5-2^{2}\times 3^{3}\times 4^{2}+10$$

Subtract 864 from 2 to get -862.

$$-\frac{862}{3}-5-2^{2}\times 3^{3}\times 4^{2}+10$$

Convert 5 to fraction \frac{15}{3}.

$$-\frac{862}{3}-\frac{15}{3}-2^{2}\times 3^{3}\times 4^{2}+10$$

Since -\frac{862}{3} and \frac{15}{3} have the same denominator, subtract them by subtracting their numerators.

$$\frac{-862-15}{3}-2^{2}\times 3^{3}\times 4^{2}+10$$

Subtract 15 from -862 to get -877.

$$-\frac{877}{3}-2^{2}\times 3^{3}\times 4^{2}+10$$

Calculate 2 to the power of 2 and get 4.

$$-\frac{877}{3}-4\times 3^{3}\times 4^{2}+10$$

Calculate 3 to the power of 3 and get 27.

$$-\frac{877}{3}-4\times 27\times 4^{2}+10$$

Multiply 4 and 27 to get 108.

$$-\frac{877}{3}-108\times 4^{2}+10$$

Calculate 4 to the power of 2 and get 16.

$$-\frac{877}{3}-108\times 16+10$$

Multiply 108 and 16 to get 1728.

$$-\frac{877}{3}-1728+10$$

Convert 1728 to fraction \frac{5184}{3}.

$$-\frac{877}{3}-\frac{5184}{3}+10$$

Since -\frac{877}{3} and \frac{5184}{3} have the same denominator, subtract them by subtracting their numerators.

$$\frac{-877-5184}{3}+10$$

Subtract 5184 from -877 to get -6061.

$$-\frac{6061}{3}+10$$

Convert 10 to fraction \frac{30}{3}.

$$-\frac{6061}{3}+\frac{30}{3}$$

Since -\frac{6061}{3} and \frac{30}{3} have the same denominator, add them by adding their numerators.

$$\frac{-6061+30}{3}$$

Add -6061 and 30 to get -6031.

$$-\frac{6031}{3}$$

Factor

$$-\frac{6031}{3} = -2010\frac{1}{3} = -2010.3333333333333$$