Solve 81^{3/4}(frac{8^frac{2{3}}9^frac{3{2}}}{32^frac{2{5}}})^frac{1{3}}

$$81 ^ { \frac { 3 } { 4 } } ( \frac { 8 ^ { \frac { 2 } { 3 } } 9 ^ { \frac { 3 } { 2 } } } { 32 ^ { \frac { 2 } { 5 } } } ) ^ { \frac { 1 } { 3 } }$$

Evaluate

$$81$$

Solution Steps

Calculate 81 to the power of \frac{3}{4} and get 27.

$$27\times \left(\frac{8^{\frac{2}{3}}\times 9^{\frac{3}{2}}}{32^{\frac{2}{5}}}\right)^{\frac{1}{3}}$$

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

$$27\times \left(\frac{4\times 9^{\frac{3}{2}}}{32^{\frac{2}{5}}}\right)^{\frac{1}{3}}$$

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

$$27\times \left(\frac{4\times 27}{32^{\frac{2}{5}}}\right)^{\frac{1}{3}}$$

Multiply 4 and 27 to get 108.

$$27\times \left(\frac{108}{32^{\frac{2}{5}}}\right)^{\frac{1}{3}}$$

Calculate 32 to the power of \frac{2}{5} and get 4.

$$27\times \left(\frac{108}{4}\right)^{\frac{1}{3}}$$

Divide 108 by 4 to get 27.

$$27\times 27^{\frac{1}{3}}$$

Calculate 27 to the power of \frac{1}{3} and get 3.

$$27\times 3$$

Multiply 27 and 3 to get 81.

$$81$$

Factor

$$3^{4}$$