Solve (x^frac{2{3}}-x^frac{1{3}})(x^frac{2{3}}+x^frac{1{3}})

$$( x ^ { \frac { 2 } { 3 } } - x ^ { \frac { 1 } { 3 } } ) ( x ^ { \frac { 2 } { 3 } } + x ^ { \frac { 1 } { 3 } } )$$

Evaluate

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

Solution Steps

Multiplication can be transformed into difference of squares using the rule: \left(a-b\right)\left(a+b\right)=a^{2}-b^{2}.

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

To raise a power to another power, multiply the exponents. Multiply \frac{2}{3} and 2 to get \frac{4}{3}.

$$x^{\frac{4}{3}}-\left(x^{\frac{1}{3}}\right)^{2}$$

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

$$x^{\frac{4}{3}}-x^{\frac{2}{3}}$$

Factor

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