Solve (2/5)^-3*(7/11)^4*(5/2)^7(11/7)^-2

$$( \frac { 2 } { 5 } ) ^ { - 3 } \cdot ( \frac { 7 } { 11 } ) ^ { 4 } \cdot ( \frac { 5 } { 2 } ) ^ { 7 } ( \frac { 11 } { 7 } ) ^ { - 2 }$$

Evaluate

$$\frac{1148916015625}{1814078464}\approx 633.333143205$$

Solution Steps

Calculate \frac{2}{5} to the power of -3 and get \frac{125}{8}.

$$\frac{125}{8}\times \left(\frac{7}{11}\right)^{4}\times \left(\frac{5}{2}\right)^{7}\times \left(\frac{11}{7}\right)^{-2}$$

Calculate \frac{7}{11} to the power of 4 and get \frac{2401}{14641}.

$$\frac{125}{8}\times \frac{2401}{14641}\times \left(\frac{5}{2}\right)^{7}\times \left(\frac{11}{7}\right)^{-2}$$

Multiply \frac{125}{8} and \frac{2401}{14641} to get \frac{300125}{117128}.

$$\frac{300125}{117128}\times \left(\frac{5}{2}\right)^{7}\times \left(\frac{11}{7}\right)^{-2}$$

Calculate \frac{5}{2} to the power of 7 and get \frac{78125}{128}.

$$\frac{300125}{117128}\times \frac{78125}{128}\times \left(\frac{11}{7}\right)^{-2}$$

Multiply \frac{300125}{117128} and \frac{78125}{128} to get \frac{23447265625}{14992384}.

$$\frac{23447265625}{14992384}\times \left(\frac{11}{7}\right)^{-2}$$

Calculate \frac{11}{7} to the power of -2 and get \frac{49}{121}.

$$\frac{23447265625}{14992384}\times \frac{49}{121}$$

Multiply \frac{23447265625}{14992384} and \frac{49}{121} to get \frac{1148916015625}{1814078464}.

$$\frac{1148916015625}{1814078464}$$

Factor

$$\frac{5 ^ {10} \cdot 7 ^ {6}}{2 ^ {10} \cdot 11 ^ {6}} = 633\frac{604347913}{1814078464} = 633.3331432046591$$