What is the limit as x approaches-2 of x^{2/3} ?

The limit as x approaches-2 of x^{2/3} is (-1)^{2/3}*2^{2/3}

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limit as x approaches-2 of x^{2/3}

x \to - 2 lim (x^{\frac{2}{3}})

(- 1)^{\frac{2}{3}} \cdot 2^{\frac{2}{3}}

Solution steps

x \to - 2 lim (x^{\frac{2}{3}})

Plug in the value

x = - 2

= (- 2)^{\frac{2}{3}}

Apply exponent rule:

(- a)^{\frac{m}{n}} = (- 1)^{\frac{m}{n}} (a)^{\frac{m}{n}}

(- 2)^{\frac{2}{3}} = (- 1)^{\frac{2}{3}} \cdot 2^{\frac{2}{3}}

= (- 1)^{\frac{2}{3}} \cdot 2^{\frac{2}{3}}

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What is the limit as x approaches-2 of x^{2/3} ?
The limit as x approaches-2 of x^{2/3} is (-1)^{2/3}*2^{2/3}