Solve (6^{3}*5^{2})^4*(5^2*6^3)^-3

$$( 6 ^ { 3 } \times 5 ^ { 2 } ) ^ { 4 } \times ( 5 ^ { 2 } \times 6 ^ { 3 } ) ^ { - 3 }$$

Evaluate

$$5400$$

Solution Steps

To multiply powers of the same base, add their exponents. Add 4 and -3 to get 1.

$$\left(6^{3}\times 5^{2}\right)^{1}$$

Calculate 6 to the power of 3 and get 216.

$$\left(216\times 5^{2}\right)^{1}$$

Calculate 5 to the power of 2 and get 25.

$$\left(216\times 25\right)^{1}$$

Multiply 216 and 25 to get 5400.

$$5400^{1}$$

Calculate 5400 to the power of 1 and get 5400.

$$5400$$

Factor

$$2^{3}\times 3^{3}\times 5^{2}$$