Solve 15^2*8^2*40/3^2*4^5*5

$$\frac { 15 ^ { 2 } \times 8 ^ { 2 } \times 40 } { 3 ^ { 2 } \times 4 ^ { 5 } \times 5 }$$

Evaluate

$$\frac{25}{2}=12.5$$

Solution Steps

Cancel out 5 in both numerator and denominator.

$$\frac{8\times 8^{2}\times 15^{2}}{3^{2}\times 4^{5}}$$

To multiply powers of the same base, add their exponents. Add 1 and 2 to get 3.

$$\frac{8^{3}\times 15^{2}}{3^{2}\times 4^{5}}$$

Calculate 8 to the power of 3 and get 512.

$$\frac{512\times 15^{2}}{3^{2}\times 4^{5}}$$

Calculate 15 to the power of 2 and get 225.

$$\frac{512\times 225}{3^{2}\times 4^{5}}$$

Multiply 512 and 225 to get 115200.

$$\frac{115200}{3^{2}\times 4^{5}}$$

Calculate 3 to the power of 2 and get 9.

$$\frac{115200}{9\times 4^{5}}$$

Calculate 4 to the power of 5 and get 1024.

$$\frac{115200}{9\times 1024}$$

Multiply 9 and 1024 to get 9216.

$$\frac{115200}{9216}$$

Reduce the fraction \frac{115200}{9216} to lowest terms by extracting and canceling out 4608.

$$\frac{25}{2}$$

Factor

$$\frac{5 ^ {2}}{2} = 12\frac{1}{2} = 12.5$$