Solve 3/4-2^13^24^3--2^2{3}^{3}{4}^2+-{2}^3{3}^2{4}^3

$$\frac{ 3 }{ 4 } - { 2 }^{ 1 } { 3 }^{ 2 } { 4 }^{ 3 } -- { 2 }^{ 2 } { 3 }^{ 3 } { 4 }^{ 2 } +- { 2 }^{ 3 } { 3 }^{ 2 } { 4 }^{ 3 }$$

Evaluate

$$-\frac{16125}{4}=-4031.25$$

Solution Steps

Calculate 2 to the power of 1 and get 2.

$$\frac{3}{4}-2\times 3^{2}\times 4^{3}-\left(-2^{2}\right)\times 3^{3}\times 4^{2}+\left(-2^{3}\right)\times 3^{2}\times 4^{3}$$

Calculate 3 to the power of 2 and get 9.

$$\frac{3}{4}-2\times 9\times 4^{3}-\left(-2^{2}\right)\times 3^{3}\times 4^{2}+\left(-2^{3}\right)\times 3^{2}\times 4^{3}$$

Multiply 2 and 9 to get 18.

$$\frac{3}{4}-18\times 4^{3}-\left(-2^{2}\right)\times 3^{3}\times 4^{2}+\left(-2^{3}\right)\times 3^{2}\times 4^{3}$$

Calculate 4 to the power of 3 and get 64.

$$\frac{3}{4}-18\times 64-\left(-2^{2}\right)\times 3^{3}\times 4^{2}+\left(-2^{3}\right)\times 3^{2}\times 4^{3}$$

Multiply 18 and 64 to get 1152.

$$\frac{3}{4}-1152-\left(-2^{2}\right)\times 3^{3}\times 4^{2}+\left(-2^{3}\right)\times 3^{2}\times 4^{3}$$

Convert 1152 to fraction \frac{4608}{4}.

$$\frac{3}{4}-\frac{4608}{4}-\left(-2^{2}\right)\times 3^{3}\times 4^{2}+\left(-2^{3}\right)\times 3^{2}\times 4^{3}$$

Since \frac{3}{4} and \frac{4608}{4} have the same denominator, subtract them by subtracting their numerators.

$$\frac{3-4608}{4}-\left(-2^{2}\right)\times 3^{3}\times 4^{2}+\left(-2^{3}\right)\times 3^{2}\times 4^{3}$$

Subtract 4608 from 3 to get -4605.

$$-\frac{4605}{4}-\left(-2^{2}\right)\times 3^{3}\times 4^{2}+\left(-2^{3}\right)\times 3^{2}\times 4^{3}$$

Calculate 2 to the power of 2 and get 4.

$$-\frac{4605}{4}-\left(-4\times 3^{3}\times 4^{2}\right)+\left(-2^{3}\right)\times 3^{2}\times 4^{3}$$

Calculate 3 to the power of 3 and get 27.

$$-\frac{4605}{4}-\left(-4\times 27\times 4^{2}\right)+\left(-2^{3}\right)\times 3^{2}\times 4^{3}$$

Multiply -4 and 27 to get -108.

$$-\frac{4605}{4}-\left(-108\times 4^{2}\right)+\left(-2^{3}\right)\times 3^{2}\times 4^{3}$$

Calculate 4 to the power of 2 and get 16.

$$-\frac{4605}{4}-\left(-108\times 16\right)+\left(-2^{3}\right)\times 3^{2}\times 4^{3}$$

Multiply -108 and 16 to get -1728.

$$-\frac{4605}{4}-\left(-1728\right)+\left(-2^{3}\right)\times 3^{2}\times 4^{3}$$

The opposite of -1728 is 1728.

$$-\frac{4605}{4}+1728+\left(-2^{3}\right)\times 3^{2}\times 4^{3}$$

Convert 1728 to fraction \frac{6912}{4}.

$$-\frac{4605}{4}+\frac{6912}{4}+\left(-2^{3}\right)\times 3^{2}\times 4^{3}$$

Since -\frac{4605}{4} and \frac{6912}{4} have the same denominator, add them by adding their numerators.

$$\frac{-4605+6912}{4}+\left(-2^{3}\right)\times 3^{2}\times 4^{3}$$

Add -4605 and 6912 to get 2307.

$$\frac{2307}{4}+\left(-2^{3}\right)\times 3^{2}\times 4^{3}$$

Calculate 2 to the power of 3 and get 8.

$$\frac{2307}{4}-8\times 3^{2}\times 4^{3}$$

Calculate 3 to the power of 2 and get 9.

$$\frac{2307}{4}-8\times 9\times 4^{3}$$

Multiply -8 and 9 to get -72.

$$\frac{2307}{4}-72\times 4^{3}$$

Calculate 4 to the power of 3 and get 64.

$$\frac{2307}{4}-72\times 64$$

Multiply -72 and 64 to get -4608.

$$\frac{2307}{4}-4608$$

Convert 4608 to fraction \frac{18432}{4}.

$$\frac{2307}{4}-\frac{18432}{4}$$

Since \frac{2307}{4} and \frac{18432}{4} have the same denominator, subtract them by subtracting their numerators.

$$\frac{2307-18432}{4}$$

Subtract 18432 from 2307 to get -16125.

$$-\frac{16125}{4}$$

Factor

$$-\frac{16125}{4} = -4031\frac{1}{4} = -4031.25$$