Solve (frac{2172^{3}17^4}{112^5/1^3})^-1

$$( \frac { 2172 ^ { 3 } 17 ^ { 4 } } { 112 ^ { 5 } / 1 ^ { 3 } } ) ^ { - 1 }$$

Evaluate

$$\frac{275365888}{13371963247647}\approx 0.000020593$$

Solution Steps

Calculate 2172 to the power of 3 and get 10246592448.

$$\left(\frac{10246592448\times 17^{4}}{\frac{112^{5}}{1^{3}}}\right)^{-1}$$

Calculate 17 to the power of 4 and get 83521.

$$\left(\frac{10246592448\times 83521}{\frac{112^{5}}{1^{3}}}\right)^{-1}$$

Multiply 10246592448 and 83521 to get 855805647849408.

$$\left(\frac{855805647849408}{\frac{112^{5}}{1^{3}}}\right)^{-1}$$

Calculate 112 to the power of 5 and get 17623416832.

$$\left(\frac{855805647849408}{\frac{17623416832}{1^{3}}}\right)^{-1}$$

Calculate 1 to the power of 3 and get 1.

$$\left(\frac{855805647849408}{\frac{17623416832}{1}}\right)^{-1}$$

Anything divided by one gives itself.

$$\left(\frac{855805647849408}{17623416832}\right)^{-1}$$

Reduce the fraction \frac{855805647849408}{17623416832} to lowest terms by extracting and canceling out 64.

$$\left(\frac{13371963247647}{275365888}\right)^{-1}$$

Calculate \frac{13371963247647}{275365888} to the power of -1 and get \frac{275365888}{13371963247647}.

$$\frac{275365888}{13371963247647}$$

Factor

$$\frac{2 ^ {14} \cdot 7 ^ {5}}{3 ^ {3} \cdot 17 ^ {4} \cdot 181 ^ {3}} = 2.05927793025048 \times 10^{-5}$$