Solve 32^3/3-42^2/2-31^3/3-41^2/2

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

Evaluate

$$-3$$

Solution Steps

To divide powers of the same base, subtract the denominator's exponent from the numerator's exponent. Subtract 1 from 2 to get 1.

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

Calculate 2 to the power of 3 and get 8.

$$3\times \frac{8}{3}-4\times 2^{1}-3\times \frac{1^{3}}{3}-4\times \frac{1^{2}}{2}$$

Cancel out 3 and 3.

$$8-4\times 2^{1}-3\times \frac{1^{3}}{3}-4\times \frac{1^{2}}{2}$$

Calculate 2 to the power of 1 and get 2.

$$8-4\times 2-3\times \frac{1^{3}}{3}-4\times \frac{1^{2}}{2}$$

Multiply 4 and 2 to get 8.

$$8-8-3\times \frac{1^{3}}{3}-4\times \frac{1^{2}}{2}$$

Subtract 8 from 8 to get 0.

$$0-3\times \frac{1^{3}}{3}-4\times \frac{1^{2}}{2}$$

Calculate 1 to the power of 3 and get 1.

$$0-3\times \frac{1}{3}-4\times \frac{1^{2}}{2}$$

Cancel out 3 and 3.

$$0-1-4\times \frac{1^{2}}{2}$$

Subtract 1 from 0 to get -1.

$$-1-4\times \frac{1^{2}}{2}$$

Calculate 1 to the power of 2 and get 1.

$$-1-4\times \frac{1}{2}$$

Multiply 4 and \frac{1}{2} to get \frac{4}{2}.

$$-1-\frac{4}{2}$$

Divide 4 by 2 to get 2.

$$-1-2$$

Subtract 2 from -1 to get -3.

$$-3$$

Factor

$$-3$$