Solve frac{(2^{4}*3^6)^frac{1{2}}*sqrt[3]{8}*sqrt{81}}{16^frac{3{4}}*27^frac{1{3}}}

$$\frac { ( 2 ^ { 4 } \times 3 ^ { 6 } ) ^ { \frac { 1 } { 2 } } \times \sqrt[ 3 ] { 8 } \times \sqrt { 81 } } { 16 ^ { \frac { 3 } { 4 } } \times 27 ^ { \frac { 1 } { 3 } } }$$

Evaluate

$$81$$

Solution Steps

Calculate 2 to the power of 4 and get 16.

$$\frac{\left(16\times 3^{6}\right)^{\frac{1}{2}}\sqrt[3]{8}\sqrt{81}}{16^{\frac{3}{4}}\times 27^{\frac{1}{3}}}$$

Calculate 3 to the power of 6 and get 729.

$$\frac{\left(16\times 729\right)^{\frac{1}{2}}\sqrt[3]{8}\sqrt{81}}{16^{\frac{3}{4}}\times 27^{\frac{1}{3}}}$$

Multiply 16 and 729 to get 11664.

$$\frac{11664^{\frac{1}{2}}\sqrt[3]{8}\sqrt{81}}{16^{\frac{3}{4}}\times 27^{\frac{1}{3}}}$$

Calculate 11664 to the power of \frac{1}{2} and get 108.

$$\frac{108\sqrt[3]{8}\sqrt{81}}{16^{\frac{3}{4}}\times 27^{\frac{1}{3}}}$$

Calculate \sqrt[3]{8} and get 2.

$$\frac{108\times 2\sqrt{81}}{16^{\frac{3}{4}}\times 27^{\frac{1}{3}}}$$

Multiply 108 and 2 to get 216.

$$\frac{216\sqrt{81}}{16^{\frac{3}{4}}\times 27^{\frac{1}{3}}}$$

Calculate the square root of 81 and get 9.

$$\frac{216\times 9}{16^{\frac{3}{4}}\times 27^{\frac{1}{3}}}$$

Multiply 216 and 9 to get 1944.

$$\frac{1944}{16^{\frac{3}{4}}\times 27^{\frac{1}{3}}}$$

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

$$\frac{1944}{8\times 27^{\frac{1}{3}}}$$

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

$$\frac{1944}{8\times 3}$$

Multiply 8 and 3 to get 24.

$$\frac{1944}{24}$$

Divide 1944 by 24 to get 81.

$$81$$

Factor

$$3^{4}$$