Solve (5*2^{2})^3:(3+2^3+3^2)^2

$$( 5 \times 2 ^ { 2 } ) ^ { 3 } : ( 3 + 2 ^ { 3 } + 3 ^ { 2 } ) ^ { 2 }$$

Evaluate

$$20$$

Solution Steps

Calculate 2 to the power of 2 and get 4.

$$\frac{\left(5\times 4\right)^{3}}{\left(3+2^{3}+3^{2}\right)^{2}}$$

Multiply 5 and 4 to get 20.

$$\frac{20^{3}}{\left(3+2^{3}+3^{2}\right)^{2}}$$

Calculate 20 to the power of 3 and get 8000.

$$\frac{8000}{\left(3+2^{3}+3^{2}\right)^{2}}$$

Calculate 2 to the power of 3 and get 8.

$$\frac{8000}{\left(3+8+3^{2}\right)^{2}}$$

Add 3 and 8 to get 11.

$$\frac{8000}{\left(11+3^{2}\right)^{2}}$$

Calculate 3 to the power of 2 and get 9.

$$\frac{8000}{\left(11+9\right)^{2}}$$

Add 11 and 9 to get 20.

$$\frac{8000}{20^{2}}$$

Calculate 20 to the power of 2 and get 400.

$$\frac{8000}{400}$$

Divide 8000 by 400 to get 20.

$$20$$

Factor

$$2^{2}\times 5$$