Solve (4/22)^10*(2/11)^12*(6/33)^7

$$( \frac { 4 } { 22 } ) ^ { 10 } \times ( \frac { 2 } { 11 } ) ^ { 12 } \times ( \frac { 6 } { 33 } ) ^ { 7 }$$

Evaluate

$$\frac{536870912}{1586309297171491574414436704891}\approx 3.38440248 \cdot 10^{-22}$$

Solution Steps

Reduce the fraction \frac{4}{22} to lowest terms by extracting and canceling out 2.

$$\left(\frac{2}{11}\right)^{10}\times \left(\frac{2}{11}\right)^{12}\times \left(\frac{6}{33}\right)^{7}$$

Calculate \frac{2}{11} to the power of 10 and get \frac{1024}{25937424601}.

$$\frac{1024}{25937424601}\times \left(\frac{2}{11}\right)^{12}\times \left(\frac{6}{33}\right)^{7}$$

Calculate \frac{2}{11} to the power of 12 and get \frac{4096}{3138428376721}.

$$\frac{1024}{25937424601}\times \frac{4096}{3138428376721}\times \left(\frac{6}{33}\right)^{7}$$

Multiply \frac{1024}{25937424601} and \frac{4096}{3138428376721} to get \frac{4194304}{81402749386839761113321}.

$$\frac{4194304}{81402749386839761113321}\times \left(\frac{6}{33}\right)^{7}$$

Reduce the fraction \frac{6}{33} to lowest terms by extracting and canceling out 3.

$$\frac{4194304}{81402749386839761113321}\times \left(\frac{2}{11}\right)^{7}$$

Calculate \frac{2}{11} to the power of 7 and get \frac{128}{19487171}.

$$\frac{4194304}{81402749386839761113321}\times \frac{128}{19487171}$$

Multiply \frac{4194304}{81402749386839761113321} and \frac{128}{19487171} to get \frac{536870912}{1586309297171491574414436704891}.

$$\frac{536870912}{1586309297171491574414436704891}$$

Factor

$$\frac{2 ^ {29}}{11 ^ {29}} = 3.3844024803818593 \times 10^{-22}$$