Given:
The expression is:
[tex]\sqrt[3]{\dfrac{-512}{729}}[/tex]
To find:
The value of the given expression.
Solution:
We have,
[tex]\sqrt[3]{\dfrac{-512}{729}}[/tex]
It can be rewritten as
[tex]=\sqrt[3]{\dfrac{(-8)\times (-8) \times (-8)}{9\times 9\times 9}}[/tex]
[tex]=\sqrt[3]{\dfrac{(-8)^3}{9^3}}[/tex] [tex][\because a^ma^n=a^{m+n}][/tex]
[tex]=\sqrt[3]{\left(\dfrac{-8}{9}\right)^3}[/tex] [tex][\because \dfrac{a^m}{b^m}=\left(\dfrac{a}{b}\right)^m][/tex]
[tex]=\dfrac{-8}{9}[/tex] [tex][\because \sqrt[n]{x^n}=x][/tex]
The value of given expression is [tex]\dfrac{-8}{9}[/tex].
Therefore, the correct option is b.
