Question

Plplpl solve the answer​

Answer 1

Given:

The expression is:

$\sqrt[3]{\dfrac{-512}{729}}$

To find:

The value of the given expression.

Solution:

We have,

$\sqrt[3]{\dfrac{-512}{729}}$

It can be rewritten as

$=\sqrt[3]{\dfrac{(-8)\times (-8) \times (-8)}{9\times 9\times 9}}$

$=\sqrt[3]{\dfrac{(-8)^3}{9^3}}$        $[\because a^ma^n=a^{m+n}]$

$=\sqrt[3]{\left(\dfrac{-8}{9}\right)^3}$        $[\because \dfrac{a^m}{b^m}=\left(\dfrac{a}{b}\right)^m]$

$=\dfrac{-8}{9}$        $[\because \sqrt[n]{x^n}=x]$

The value of given expression is $\dfrac{-8}{9}$.

Therefore, the correct option is b.