Solve left(lceil4^7*4^10*4rceilright)^4div{left(4^5right)}^7

$${ \left( \lceil { 4 }^{ 7 } \times { 4 }^{ 10 } \times 4 \rceil \right) }^{ 4 } \div { \left( { 4 }^{ 5 } \right) }^{ 7 }$$

Evaluate

$$18889465931478580854784$$

Solution Steps

To multiply powers of the same base, add their exponents. Add 7 and 10 to get 17.

$$\frac{\left(\lceil 4^{17}\times 4\rceil \right)^{4}}{\left(4^{5}\right)^{7}}$$

To multiply powers of the same base, add their exponents. Add 17 and 1 to get 18.

$$\frac{\left(\lceil 4^{18}\rceil \right)^{4}}{\left(4^{5}\right)^{7}}$$

To raise a power to another power, multiply the exponents. Multiply 5 and 7 to get 35.

$$\frac{\left(\lceil 4^{18}\rceil \right)^{4}}{4^{35}}$$

Calculate 4 to the power of 18 and get 68719476736.

$$\frac{\left(\lceil 68719476736\rceil \right)^{4}}{4^{35}}$$

The ceiling of a real number a is the smallest integer number greater than or equal to a. The ceiling of 68719476736 is 68719476736.

$$\frac{68719476736^{4}}{4^{35}}$$

Calculate 68719476736 to the power of 4 and get 22300745198530623141535718272648361505980416.

$$\frac{22300745198530623141535718272648361505980416}{4^{35}}$$

Calculate 4 to the power of 35 and get 1180591620717411303424.

$$\frac{22300745198530623141535718272648361505980416}{1180591620717411303424}$$

Divide 22300745198530623141535718272648361505980416 by 1180591620717411303424 to get 18889465931478580854784.

$$18889465931478580854784$$

Factor

$$2^{74}$$