Solve a(4^21-5^20)/4(4^20-5^20)

$$\frac { a ( 4 ^ { 21 } - 5 ^ { 20 } ) } { 4 ( 4 ^ { 20 } - 5 ^ { 20 } ) }$$

Evaluate

$$\frac{30323128376507a}{125690560017132}$$

Solution Steps

Calculate 4 to the power of 21 and get 4398046511104.

$$\frac{a\left(4398046511104-5^{20}\right)}{4\left(4^{20}-5^{20}\right)}$$

Calculate 5 to the power of 20 and get 95367431640625.

$$\frac{a\left(4398046511104-95367431640625\right)}{4\left(4^{20}-5^{20}\right)}$$

Subtract 95367431640625 from 4398046511104 to get -90969385129521.

$$\frac{a\left(-90969385129521\right)}{4\left(4^{20}-5^{20}\right)}$$

Calculate 4 to the power of 20 and get 1099511627776.

$$\frac{a\left(-90969385129521\right)}{4\left(1099511627776-5^{20}\right)}$$

Calculate 5 to the power of 20 and get 95367431640625.

$$\frac{a\left(-90969385129521\right)}{4\left(1099511627776-95367431640625\right)}$$

Subtract 95367431640625 from 1099511627776 to get -94267920012849.

$$\frac{a\left(-90969385129521\right)}{4\left(-94267920012849\right)}$$

Multiply 4 and -94267920012849 to get -377071680051396.

$$\frac{a\left(-90969385129521\right)}{-377071680051396}$$

Divide a\left(-90969385129521\right) by -377071680051396 to get a\times \frac{30323128376507}{125690560017132}.

$$a\times \frac{30323128376507}{125690560017132}$$

Expand

$$\frac{30323128376507a}{125690560017132}$$

Solution Steps

Calculate 4 to the power of 21 and get 4398046511104.

$$\frac{a\left(4398046511104-5^{20}\right)}{4\left(4^{20}-5^{20}\right)}$$

Calculate 5 to the power of 20 and get 95367431640625.

$$\frac{a\left(4398046511104-95367431640625\right)}{4\left(4^{20}-5^{20}\right)}$$

Subtract 95367431640625 from 4398046511104 to get -90969385129521.

$$\frac{a\left(-90969385129521\right)}{4\left(4^{20}-5^{20}\right)}$$

Calculate 4 to the power of 20 and get 1099511627776.

$$\frac{a\left(-90969385129521\right)}{4\left(1099511627776-5^{20}\right)}$$

Calculate 5 to the power of 20 and get 95367431640625.

$$\frac{a\left(-90969385129521\right)}{4\left(1099511627776-95367431640625\right)}$$

Subtract 95367431640625 from 1099511627776 to get -94267920012849.

$$\frac{a\left(-90969385129521\right)}{4\left(-94267920012849\right)}$$

Multiply 4 and -94267920012849 to get -377071680051396.

$$\frac{a\left(-90969385129521\right)}{-377071680051396}$$

Divide a\left(-90969385129521\right) by -377071680051396 to get a\times \frac{30323128376507}{125690560017132}.

$$a\times \frac{30323128376507}{125690560017132}$$