Solve frac{4^{3}*9^{3}+6^3*120}{8^4*3^12-6^11}

$$\frac { 4 ^ { 3 } \cdot 9 ^ { 3 } + 6 ^ { 3 } \cdot 120 } { 8 ^ { 4 } \cdot 3 ^ { 12 } - 6 ^ { 11 } }$$

Evaluate

$$\frac{7}{174960}\approx 0.000040009$$

Solution Steps

Calculate 4 to the power of 3 and get 64.

$$\frac{64\times 9^{3}+6^{3}\times 120}{8^{4}\times 3^{12}-6^{11}}$$

Calculate 9 to the power of 3 and get 729.

$$\frac{64\times 729+6^{3}\times 120}{8^{4}\times 3^{12}-6^{11}}$$

Multiply 64 and 729 to get 46656.

$$\frac{46656+6^{3}\times 120}{8^{4}\times 3^{12}-6^{11}}$$

Calculate 6 to the power of 3 and get 216.

$$\frac{46656+216\times 120}{8^{4}\times 3^{12}-6^{11}}$$

Multiply 216 and 120 to get 25920.

$$\frac{46656+25920}{8^{4}\times 3^{12}-6^{11}}$$

Add 46656 and 25920 to get 72576.

$$\frac{72576}{8^{4}\times 3^{12}-6^{11}}$$

Calculate 8 to the power of 4 and get 4096.

$$\frac{72576}{4096\times 3^{12}-6^{11}}$$

Calculate 3 to the power of 12 and get 531441.

$$\frac{72576}{4096\times 531441-6^{11}}$$

Multiply 4096 and 531441 to get 2176782336.

$$\frac{72576}{2176782336-6^{11}}$$

Calculate 6 to the power of 11 and get 362797056.

$$\frac{72576}{2176782336-362797056}$$

Subtract 362797056 from 2176782336 to get 1813985280.

$$\frac{72576}{1813985280}$$

Reduce the fraction \frac{72576}{1813985280} to lowest terms by extracting and canceling out 10368.

$$\frac{7}{174960}$$

Factor

$$\frac{7}{2 ^ {4} \cdot 3 ^ {7} \cdot 5} = 4.000914494741655 \times 10^{-5}$$