Answer:
The cube root of 512 is 8
Explanation:
The cube root of a number is expressed in radical form as;
![\sqrt[3]{x}](https://img.qammunity.org/2020/formulas/mathematics/high-school/adp5h6zbpgyn5rixh96ki4nbf91jilhd94.png)
Using exponents, the above expression is equivalent to;
![x^{(1)/(3)}](https://img.qammunity.org/2020/formulas/mathematics/high-school/5ofosmndneyyvzrgyi033k20hjb1gum0e4.png)
512 can be expressed as;
2*2*2*2*2*2*2*2*2
This is equivalent to;
![2^(9)](https://img.qammunity.org/2020/formulas/mathematics/middle-school/iumekfpw2o8usxfadpcu78nsjr3lq6jcvp.png)
Therefore;
![512^{(1)/(3) }=(2^(9))^{(1)/(3) }=2^(3)=8](https://img.qammunity.org/2020/formulas/mathematics/middle-school/zdx148y5ml0kl8zdi77z8qurncolnnofui.png)
The cube root of 512 is thus 8