Solve (75)^10*(27)^16/(36)^24*(10)^20

$$\frac { ( 75 ) ^ { 10 } \times ( 27 ) ^ { 16 } } { ( 36 ) ^ { 24 } \times ( 10 ) ^ { 20 } }$$

Evaluate

$$\frac{59049}{295147905179352825856}=2.00065794 \cdot 10^{-16}$$

Solution Steps

Calculate 75 to the power of 10 and get 5631351470947265625.

$$\frac{5631351470947265625\times 27^{16}}{36^{24}\times 10^{20}}$$

Calculate 27 to the power of 16 and get 79766443076872509863361.

$$\frac{5631351470947265625\times 79766443076872509863361}{36^{24}\times 10^{20}}$$

Multiply 5631351470947265625 and 79766443076872509863361 to get 449192876553177340976868027591705322265625.

$$\frac{449192876553177340976868027591705322265625}{36^{24}\times 10^{20}}$$

Calculate 36 to the power of 24 and get 22452257707354557240087211123792674816.

$$\frac{449192876553177340976868027591705322265625}{22452257707354557240087211123792674816\times 10^{20}}$$

Calculate 10 to the power of 20 and get 100000000000000000000.

$$\frac{449192876553177340976868027591705322265625}{22452257707354557240087211123792674816\times 100000000000000000000}$$

Multiply 22452257707354557240087211123792674816 and 100000000000000000000 to get 2245225770735455724008721112379267481600000000000000000000.

$$\frac{449192876553177340976868027591705322265625}{2245225770735455724008721112379267481600000000000000000000}$$

Reduce the fraction \frac{449192876553177340976868027591705322265625}{2245225770735455724008721112379267481600000000000000000000} to lowest terms by extracting and canceling out 7607120807349444376312351226806640625.

$$\frac{59049}{295147905179352825856}$$

Factor

$$\frac{3 ^ {10}}{2 ^ {68}} = 2.0006579400967675 \times 10^{-16}$$