Simplify $\left(\dfrac{2}{x} ight)^{3}$ for $x
e 0$.

Question

Simplify $\left(\dfrac{2}{x}ight)^{3}$ for $x 
e 0$.

Accepted Answer

A. $\dfrac{8}{x^{3}}$

Apply $\left(\dfrac{a}{b}\right)^{n} = \dfrac{a^{n}}{b^{n}}$:
$\left(\dfrac{2}{x}\right)^{3} = \dfrac{2^{3}}{x^{3}} = \dfrac{8}{x^{3}}$.
- Trap B ($6 = 2 \cdot 3$) treats $2^3$ as $2 \cdot 3$.
- Trap C only cubes the denominator.

Answer

$\dfrac{2}{x^{3}}$

Answer

$\dfrac{8}{3x}$

Answer

$\dfrac{6}{x^{3}}$

Simplify $\left(\dfrac{2}{x}\right)^{3}$ for $x \ne 0$.