Solve (3+3+3+3)^3/(3+3+3)^3

$$\frac { ( 3 + 3 + 3 + 3 ) ^ { 3 } } { ( 3 + 3 + 3 ) ^ { 3 } }$$

Evaluate

$$\frac{64}{27}\approx 2.37037037$$

Solution Steps

Add 3 and 3 to get 6.

$$\frac{\left(6+3+3\right)^{3}}{\left(3+3+3\right)^{3}}$$

Add 6 and 3 to get 9.

$$\frac{\left(9+3\right)^{3}}{\left(3+3+3\right)^{3}}$$

Add 9 and 3 to get 12.

$$\frac{12^{3}}{\left(3+3+3\right)^{3}}$$

Calculate 12 to the power of 3 and get 1728.

$$\frac{1728}{\left(3+3+3\right)^{3}}$$

Add 3 and 3 to get 6.

$$\frac{1728}{\left(6+3\right)^{3}}$$

Add 6 and 3 to get 9.

$$\frac{1728}{9^{3}}$$

Calculate 9 to the power of 3 and get 729.

$$\frac{1728}{729}$$

Reduce the fraction \frac{1728}{729} to lowest terms by extracting and canceling out 27.

$$\frac{64}{27}$$

Factor

$$\frac{2 ^ {6}}{3 ^ {3}} = 2\frac{10}{27} = 2.3703703703703702$$