Solve {left(4^5/121^-2*8right)}^511^-7/16^-3

$${ \left( \frac{ { 4 }^{ 5 } }{ { 121 }^{ -2 } \times 8 } \right) }^{ 5 } \frac{ { 11 }^{ -7 } }{ { 16 }^{ -3 } }$$

Evaluate

$$4858639798350829646006714368$$

Solution Steps

Calculate 4 to the power of 5 and get 1024.

$$\left(\frac{1024}{121^{-2}\times 8}\right)^{5}\times \frac{11^{-7}}{16^{-3}}$$

Calculate 121 to the power of -2 and get \frac{1}{14641}.

$$\left(\frac{1024}{\frac{1}{14641}\times 8}\right)^{5}\times \frac{11^{-7}}{16^{-3}}$$

Multiply \frac{1}{14641} and 8 to get \frac{8}{14641}.

$$\left(\frac{1024}{\frac{8}{14641}}\right)^{5}\times \frac{11^{-7}}{16^{-3}}$$

Divide 1024 by \frac{8}{14641} by multiplying 1024 by the reciprocal of \frac{8}{14641}.

$$\left(1024\times \frac{14641}{8}\right)^{5}\times \frac{11^{-7}}{16^{-3}}$$

Multiply 1024 and \frac{14641}{8} to get 1874048.

$$1874048^{5}\times \frac{11^{-7}}{16^{-3}}$$

Calculate 1874048 to the power of 5 and get 23115513812956087720606032723968.

$$23115513812956087720606032723968\times \frac{11^{-7}}{16^{-3}}$$

Calculate 11 to the power of -7 and get \frac{1}{19487171}.

$$23115513812956087720606032723968\times \frac{\frac{1}{19487171}}{16^{-3}}$$

Calculate 16 to the power of -3 and get \frac{1}{4096}.

$$23115513812956087720606032723968\times \frac{\frac{1}{19487171}}{\frac{1}{4096}}$$

Divide \frac{1}{19487171} by \frac{1}{4096} by multiplying \frac{1}{19487171} by the reciprocal of \frac{1}{4096}.

$$23115513812956087720606032723968\times \frac{1}{19487171}\times 4096$$

Multiply \frac{1}{19487171} and 4096 to get \frac{4096}{19487171}.

$$23115513812956087720606032723968\times \frac{4096}{19487171}$$

Multiply 23115513812956087720606032723968 and \frac{4096}{19487171} to get 4858639798350829646006714368.

$$4858639798350829646006714368$$

Factor

$$2^{47}\times 11^{13}$$