Solve 18^6*6^4/108^5:(2,6-12/3)

$$\frac { 18 ^ { 6 } \cdot 6 ^ { 4 } } { 108 ^ { 5 } } : ( 2,6 - 1 \frac { 2 } { 3 } )$$

Evaluate

$$\frac{45}{14}\approx 3,214285714$$

Solution Steps

Calculate 18 to the power of 6 and get 34012224.

$$\frac{\frac{34012224\times 6^{4}}{108^{5}}}{2,6-\frac{1\times 3+2}{3}}$$

Calculate 6 to the power of 4 and get 1296.

$$\frac{\frac{34012224\times 1296}{108^{5}}}{2,6-\frac{1\times 3+2}{3}}$$

Multiply 34012224 and 1296 to get 44079842304.

$$\frac{\frac{44079842304}{108^{5}}}{2,6-\frac{1\times 3+2}{3}}$$

Calculate 108 to the power of 5 and get 14693280768.

$$\frac{\frac{44079842304}{14693280768}}{2,6-\frac{1\times 3+2}{3}}$$

Divide 44079842304 by 14693280768 to get 3.

$$\frac{3}{2,6-\frac{1\times 3+2}{3}}$$

Multiply 1 and 3 to get 3.

$$\frac{3}{2,6-\frac{3+2}{3}}$$

Add 3 and 2 to get 5.

$$\frac{3}{2,6-\frac{5}{3}}$$

Convert decimal number 2,6 to fraction \frac{26}{10}. Reduce the fraction \frac{26}{10} to lowest terms by extracting and canceling out 2.

$$\frac{3}{\frac{13}{5}-\frac{5}{3}}$$

Least common multiple of 5 and 3 is 15. Convert \frac{13}{5} and \frac{5}{3} to fractions with denominator 15.

$$\frac{3}{\frac{39}{15}-\frac{25}{15}}$$

Since \frac{39}{15} and \frac{25}{15} have the same denominator, subtract them by subtracting their numerators.

$$\frac{3}{\frac{39-25}{15}}$$

Subtract 25 from 39 to get 14.

$$\frac{3}{\frac{14}{15}}$$

Divide 3 by \frac{14}{15} by multiplying 3 by the reciprocal of \frac{14}{15}.

$$3\times \frac{15}{14}$$

Express 3\times \frac{15}{14} as a single fraction.

$$\frac{3\times 15}{14}$$

Multiply 3 and 15 to get 45.

$$\frac{45}{14}$$

Factor

$$\frac{5 \cdot 3 ^ {2}}{2 \cdot 7} = 3\frac{3}{14} = 3.2142857142857144$$