Solve 6*288/3-144/9*frac{6^{2}}{2}-96/3*6^2/2+frac{48}{9}*frac{6^3}{3}+frac{2*6^3}{3*3}-frac{1}{9}*frac{6^4}{4}

$$6 \cdot \frac { 288 } { 3 } - \frac { 144 } { 9 } \cdot \frac { 6 ^ { 2 } } { 2 } - \frac { 96 } { 3 } \cdot \frac { 6 ^ { 2 } } { 2 } + \frac { 48 } { 9 } \cdot \frac { 6 ^ { 3 } } { 3 } + \frac { 2 \cdot 6 ^ { 3 } } { 3 \cdot 3 } - \frac { 1 } { 9 } \cdot \frac { 6 ^ { 4 } } { 4 }$$

Evaluate

$$108$$

Solution Steps

Divide 288 by 3 to get 96.

$$6\times 96-\frac{144}{9}\times \frac{6^{2}}{2}-\frac{96}{3}\times \frac{6^{2}}{2}+\frac{48}{9}\times \frac{6^{3}}{3}+\frac{2\times 6^{3}}{3\times 3}-\frac{1}{9}\times \frac{6^{4}}{4}$$

Multiply 6 and 96 to get 576.

$$576-\frac{144}{9}\times \frac{6^{2}}{2}-\frac{96}{3}\times \frac{6^{2}}{2}+\frac{48}{9}\times \frac{6^{3}}{3}+\frac{2\times 6^{3}}{3\times 3}-\frac{1}{9}\times \frac{6^{4}}{4}$$

Divide 144 by 9 to get 16.

$$576-16\times \frac{6^{2}}{2}-\frac{96}{3}\times \frac{6^{2}}{2}+\frac{48}{9}\times \frac{6^{3}}{3}+\frac{2\times 6^{3}}{3\times 3}-\frac{1}{9}\times \frac{6^{4}}{4}$$

Calculate 6 to the power of 2 and get 36.

$$576-16\times \frac{36}{2}-\frac{96}{3}\times \frac{6^{2}}{2}+\frac{48}{9}\times \frac{6^{3}}{3}+\frac{2\times 6^{3}}{3\times 3}-\frac{1}{9}\times \frac{6^{4}}{4}$$

Divide 36 by 2 to get 18.

$$576-16\times 18-\frac{96}{3}\times \frac{6^{2}}{2}+\frac{48}{9}\times \frac{6^{3}}{3}+\frac{2\times 6^{3}}{3\times 3}-\frac{1}{9}\times \frac{6^{4}}{4}$$

Multiply 16 and 18 to get 288.

$$576-288-\frac{96}{3}\times \frac{6^{2}}{2}+\frac{48}{9}\times \frac{6^{3}}{3}+\frac{2\times 6^{3}}{3\times 3}-\frac{1}{9}\times \frac{6^{4}}{4}$$

Subtract 288 from 576 to get 288.

$$288-\frac{96}{3}\times \frac{6^{2}}{2}+\frac{48}{9}\times \frac{6^{3}}{3}+\frac{2\times 6^{3}}{3\times 3}-\frac{1}{9}\times \frac{6^{4}}{4}$$

Divide 96 by 3 to get 32.

$$288-32\times \frac{6^{2}}{2}+\frac{48}{9}\times \frac{6^{3}}{3}+\frac{2\times 6^{3}}{3\times 3}-\frac{1}{9}\times \frac{6^{4}}{4}$$

Calculate 6 to the power of 2 and get 36.

$$288-32\times \frac{36}{2}+\frac{48}{9}\times \frac{6^{3}}{3}+\frac{2\times 6^{3}}{3\times 3}-\frac{1}{9}\times \frac{6^{4}}{4}$$

Divide 36 by 2 to get 18.

$$288-32\times 18+\frac{48}{9}\times \frac{6^{3}}{3}+\frac{2\times 6^{3}}{3\times 3}-\frac{1}{9}\times \frac{6^{4}}{4}$$

Multiply 32 and 18 to get 576.

$$288-576+\frac{48}{9}\times \frac{6^{3}}{3}+\frac{2\times 6^{3}}{3\times 3}-\frac{1}{9}\times \frac{6^{4}}{4}$$

Subtract 576 from 288 to get -288.

$$-288+\frac{48}{9}\times \frac{6^{3}}{3}+\frac{2\times 6^{3}}{3\times 3}-\frac{1}{9}\times \frac{6^{4}}{4}$$

Reduce the fraction \frac{48}{9} to lowest terms by extracting and canceling out 3.

$$-288+\frac{16}{3}\times \frac{6^{3}}{3}+\frac{2\times 6^{3}}{3\times 3}-\frac{1}{9}\times \frac{6^{4}}{4}$$

Calculate 6 to the power of 3 and get 216.

$$-288+\frac{16}{3}\times \frac{216}{3}+\frac{2\times 6^{3}}{3\times 3}-\frac{1}{9}\times \frac{6^{4}}{4}$$

Divide 216 by 3 to get 72.

$$-288+\frac{16}{3}\times 72+\frac{2\times 6^{3}}{3\times 3}-\frac{1}{9}\times \frac{6^{4}}{4}$$

Express \frac{16}{3}\times 72 as a single fraction.

$$-288+\frac{16\times 72}{3}+\frac{2\times 6^{3}}{3\times 3}-\frac{1}{9}\times \frac{6^{4}}{4}$$

Multiply 16 and 72 to get 1152.

$$-288+\frac{1152}{3}+\frac{2\times 6^{3}}{3\times 3}-\frac{1}{9}\times \frac{6^{4}}{4}$$

Divide 1152 by 3 to get 384.

$$-288+384+\frac{2\times 6^{3}}{3\times 3}-\frac{1}{9}\times \frac{6^{4}}{4}$$

Add -288 and 384 to get 96.

$$96+\frac{2\times 6^{3}}{3\times 3}-\frac{1}{9}\times \frac{6^{4}}{4}$$

Calculate 6 to the power of 3 and get 216.

$$96+\frac{2\times 216}{3\times 3}-\frac{1}{9}\times \frac{6^{4}}{4}$$

Multiply 2 and 216 to get 432.

$$96+\frac{432}{3\times 3}-\frac{1}{9}\times \frac{6^{4}}{4}$$

Multiply 3 and 3 to get 9.

$$96+\frac{432}{9}-\frac{1}{9}\times \frac{6^{4}}{4}$$

Divide 432 by 9 to get 48.

$$96+48-\frac{1}{9}\times \frac{6^{4}}{4}$$

Add 96 and 48 to get 144.

$$144-\frac{1}{9}\times \frac{6^{4}}{4}$$

Calculate 6 to the power of 4 and get 1296.

$$144-\frac{1}{9}\times \frac{1296}{4}$$

Divide 1296 by 4 to get 324.

$$144-\frac{1}{9}\times 324$$

Multiply \frac{1}{9} and 324 to get \frac{324}{9}.

$$144-\frac{324}{9}$$

Divide 324 by 9 to get 36.

$$144-36$$

Subtract 36 from 144 to get 108.

$$108$$

Factor

$$2^{2}\times 3^{3}$$