Solve frac{32^frac{3{5}}*27^frac{2{3}}}{8^frac{2{3}}*81^frac{1{4}}}

$$\frac { 32 ^ { \frac { 3 } { 5 } } \cdot 27 ^ { \frac { 2 } { 3 } } } { 8 ^ { \frac { 2 } { 3 } } \cdot 81 ^ { \frac { 1 } { 4 } } }$$

Evaluate

$$6$$

Solution Steps

Calculate 32 to the power of \frac{3}{5} and get 8.

$$\frac{8\times 27^{\frac{2}{3}}}{8^{\frac{2}{3}}\times 81^{\frac{1}{4}}}$$

Calculate 27 to the power of \frac{2}{3} and get 9.

$$\frac{8\times 9}{8^{\frac{2}{3}}\times 81^{\frac{1}{4}}}$$

Multiply 8 and 9 to get 72.

$$\frac{72}{8^{\frac{2}{3}}\times 81^{\frac{1}{4}}}$$

Calculate 8 to the power of \frac{2}{3} and get 4.

$$\frac{72}{4\times 81^{\frac{1}{4}}}$$

Calculate 81 to the power of \frac{1}{4} and get 3.

$$\frac{72}{4\times 3}$$

Multiply 4 and 3 to get 12.

$$\frac{72}{12}$$

Divide 72 by 12 to get 6.

$$6$$

Factor

$$2\times 3$$