Solve frac{(x^{3})^{-1/9}*(x^frac{1{3}})^2}{(x^frac{1{6}})^2}

$$\frac { ( x ^ { 3 } ) ^ { - \frac { 1 } { 9 } } \cdot ( x ^ { \frac { 1 } { 3 } } ) ^ { 2 } } { ( x ^ { \frac { 1 } { 6 } } ) ^ { 2 } }$$

Evaluate

$$1$$

Solution Steps

To raise a power to another power, multiply the exponents. Multiply 3 and -\frac{1}{9} to get -\frac{1}{3}.

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

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

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

To multiply powers of the same base, add their exponents. Add -\frac{1}{3} and \frac{2}{3} to get \frac{1}{3}.

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

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

$$\frac{x^{\frac{1}{3}}}{x^{\frac{1}{3}}}$$

Divide x^{\frac{1}{3}} by x^{\frac{1}{3}} to get 1.

$$1$$

Factor

$$1$$