Solve 4^{18}div2^16*[16^2div(2^2)^5]

$$4 ^ { 18 } \div 2 ^ { 16 } \times [ 16 ^ { 2 } \div ( 2 ^ { 2 } ) ^ { 5 } ]$$

Evaluate

$$262144$$

Solution Steps

To raise a power to another power, multiply the exponents. Multiply 2 and 5 to get 10.

$$\frac{4^{18}}{2^{16}}\times \frac{16^{2}}{2^{10}}$$

Calculate 4 to the power of 18 and get 68719476736.

$$\frac{68719476736}{2^{16}}\times \frac{16^{2}}{2^{10}}$$

Calculate 2 to the power of 16 and get 65536.

$$\frac{68719476736}{65536}\times \frac{16^{2}}{2^{10}}$$

Divide 68719476736 by 65536 to get 1048576.

$$1048576\times \frac{16^{2}}{2^{10}}$$

Calculate 16 to the power of 2 and get 256.

$$1048576\times \frac{256}{2^{10}}$$

Calculate 2 to the power of 10 and get 1024.

$$1048576\times \frac{256}{1024}$$

Reduce the fraction \frac{256}{1024} to lowest terms by extracting and canceling out 256.

$$1048576\times \frac{1}{4}$$

Multiply 1048576 and \frac{1}{4} to get 262144.

$$262144$$

Factor

$$2^{18}$$