Solve 25^2*4^7/2^9+5^4

$$\frac{ { 25 }^{ 2 } \times { 4 }^{ 7 } }{ { 2 }^{ 9 } + { 5 }^{ 4 } }$$

Evaluate

$$\frac{10240000}{1137}\approx 9006.156552331$$

Solution Steps

Calculate 25 to the power of 2 and get 625.

$$\frac{625\times 4^{7}}{2^{9}+5^{4}}$$

Calculate 4 to the power of 7 and get 16384.

$$\frac{625\times 16384}{2^{9}+5^{4}}$$

Multiply 625 and 16384 to get 10240000.

$$\frac{10240000}{2^{9}+5^{4}}$$

Calculate 2 to the power of 9 and get 512.

$$\frac{10240000}{512+5^{4}}$$

Calculate 5 to the power of 4 and get 625.

$$\frac{10240000}{512+625}$$

Add 512 and 625 to get 1137.

$$\frac{10240000}{1137}$$

Factor

$$\frac{2 ^ {14} \cdot 5 ^ {4}}{3 \cdot 379} = 9006\frac{178}{1137} = 9006.156552330694$$