Solve frac{(81)^frac{1{4}}*(64)^frac{4{3}}}{(-27)^2/3*(-8)^2/3}

$$\frac { ( 81 ) ^ { \frac { 1 } { 4 } } \times ( 64 ) ^ { \frac { 4 } { 3 } } } { ( - 27 ) ^ { 2 / 3 } \times ( - 8 ) ^ { 2 } / 3 }$$

Evaluate

$$4$$

Solution Steps

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

$$\frac{3\times 64^{\frac{4}{3}}}{\frac{\left(-27\right)^{\frac{2}{3}}\left(-8\right)^{2}}{3}}$$

Calculate 64 to the power of \frac{4}{3} and get 256.

$$\frac{3\times 256}{\frac{\left(-27\right)^{\frac{2}{3}}\left(-8\right)^{2}}{3}}$$

Multiply 3 and 256 to get 768.

$$\frac{768}{\frac{\left(-27\right)^{\frac{2}{3}}\left(-8\right)^{2}}{3}}$$

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

$$\frac{768}{\frac{9\left(-8\right)^{2}}{3}}$$

Calculate -8 to the power of 2 and get 64.

$$\frac{768}{\frac{9\times 64}{3}}$$

Multiply 9 and 64 to get 576.

$$\frac{768}{\frac{576}{3}}$$

Divide 576 by 3 to get 192.

$$\frac{768}{192}$$

Divide 768 by 192 to get 4.

$$4$$

Factor

$$2^{2}$$