Solve (25)^3/2*(243)^3/5/(16)^5/4*(8)^4/3

$$\frac { ( 25 ) ^ { 3 / 2 } \times ( 243 ) ^ { 3 / 5 } } { ( 16 ) ^ { 5 / 4 } \times ( 8 ) ^ { 4 / 3 } }$$

Evaluate

$$\frac{3375}{512}=6.591796875$$

Solution Steps

Calculate 25 to the power of \frac{3}{2} and get 125.

$$\frac{125\times 243^{\frac{3}{5}}}{16^{\frac{5}{4}}\times 8^{\frac{4}{3}}}$$

Calculate 243 to the power of \frac{3}{5} and get 27.

$$\frac{125\times 27}{16^{\frac{5}{4}}\times 8^{\frac{4}{3}}}$$

Multiply 125 and 27 to get 3375.

$$\frac{3375}{16^{\frac{5}{4}}\times 8^{\frac{4}{3}}}$$

Calculate 16 to the power of \frac{5}{4} and get 32.

$$\frac{3375}{32\times 8^{\frac{4}{3}}}$$

Calculate 8 to the power of \frac{4}{3} and get 16.

$$\frac{3375}{32\times 16}$$

Multiply 32 and 16 to get 512.

$$\frac{3375}{512}$$

Factor

$$\frac{3 ^ {3} \cdot 5 ^ {3}}{2 ^ {9}} = 6\frac{303}{512} = 6.591796875$$