Solve 16^frac{1{2}}*8^-4*3^7frac{5{5}}div81

$$16 ^ { \frac { 1 } { 2 } } \times 8 ^ { - 4 } \times 3 ^ { 7 \frac { 5 } { 5 } } \div 81$$

Evaluate

$$\frac{81}{1024}=0.079101562$$

Solution Steps

Calculate 16 to the power of \frac{1}{2} and get 4.

$$\frac{4\times 8^{-4}\times 3^{\frac{7\times 5+5}{5}}}{81}$$

Calculate 8 to the power of -4 and get \frac{1}{4096}.

$$\frac{4\times \frac{1}{4096}\times 3^{\frac{7\times 5+5}{5}}}{81}$$

Multiply 4 and \frac{1}{4096} to get \frac{1}{1024}.

$$\frac{\frac{1}{1024}\times 3^{\frac{7\times 5+5}{5}}}{81}$$

Multiply 7 and 5 to get 35.

$$\frac{\frac{1}{1024}\times 3^{\frac{35+5}{5}}}{81}$$

Add 35 and 5 to get 40.

$$\frac{\frac{1}{1024}\times 3^{\frac{40}{5}}}{81}$$

Divide 40 by 5 to get 8.

$$\frac{\frac{1}{1024}\times 3^{8}}{81}$$

Calculate 3 to the power of 8 and get 6561.

$$\frac{\frac{1}{1024}\times 6561}{81}$$

Multiply \frac{1}{1024} and 6561 to get \frac{6561}{1024}.

$$\frac{\frac{6561}{1024}}{81}$$

Express \frac{\frac{6561}{1024}}{81} as a single fraction.

$$\frac{6561}{1024\times 81}$$

Multiply 1024 and 81 to get 82944.

$$\frac{6561}{82944}$$

Reduce the fraction \frac{6561}{82944} to lowest terms by extracting and canceling out 81.

$$\frac{81}{1024}$$

Factor

$$\frac{3 ^ {4}}{2 ^ {10}} = 0.0791015625$$