Solve (2^frac{1{3}}*3^-frac{1{2}})^6

$$( 2 ^ { \frac { 1 } { 3 } } \times 3 ^ { - \frac { 1 } { 2 } } ) ^ { 6 }$$

Evaluate

$$\frac{4}{27}\approx 0.148148148$$

Solution Steps

Expand \left(2^{\frac{1}{3}}\times 3^{-\frac{1}{2}}\right)^{6}.

$$\left(2^{\frac{1}{3}}\right)^{6}\times \left(3^{-\frac{1}{2}}\right)^{6}$$

To raise a power to another power, multiply the exponents. Multiply \frac{1}{3} and 6 to get 2.

$$2^{2}\times \left(3^{-\frac{1}{2}}\right)^{6}$$

To raise a power to another power, multiply the exponents. Multiply -\frac{1}{2} and 6 to get -3.

$$2^{2}\times 3^{-3}$$

Calculate 2 to the power of 2 and get 4.

$$4\times 3^{-3}$$

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

$$4\times \frac{1}{27}$$

Multiply 4 and \frac{1}{27} to get \frac{4}{27}.

$$\frac{4}{27}$$

Factor

$$\frac{2 ^ {2}}{3 ^ {3}} = 0.14814814814814814$$