Solve (frac{5^{4}*2^7*5^2}{3^2*4^2})

$$( \frac { 5 ^ { 4 } \times 2 ^ { 7 } \times 5 ^ { 2 } } { 3 ^ { 2 } \times 4 ^ { 2 } } )$$

Evaluate

$$\frac{125000}{9}\approx 13888.888888889$$

Solution Steps

To multiply powers of the same base, add their exponents. Add 4 and 2 to get 6.

$$\frac{5^{6}\times 2^{7}}{3^{2}\times 4^{2}}$$

Calculate 5 to the power of 6 and get 15625.

$$\frac{15625\times 2^{7}}{3^{2}\times 4^{2}}$$

Calculate 2 to the power of 7 and get 128.

$$\frac{15625\times 128}{3^{2}\times 4^{2}}$$

Multiply 15625 and 128 to get 2000000.

$$\frac{2000000}{3^{2}\times 4^{2}}$$

Calculate 3 to the power of 2 and get 9.

$$\frac{2000000}{9\times 4^{2}}$$

Calculate 4 to the power of 2 and get 16.

$$\frac{2000000}{9\times 16}$$

Multiply 9 and 16 to get 144.

$$\frac{2000000}{144}$$

Reduce the fraction \frac{2000000}{144} to lowest terms by extracting and canceling out 16.

$$\frac{125000}{9}$$

Factor

$$\frac{2 ^ {3} \cdot 5 ^ {6}}{3 ^ {2}} = 13888\frac{8}{9} = 13888.888888888889$$