which expression is equivalent to $(x^{1/2}y^{-2/3})^{-6}$? a $\frac{x^{3}}{y^{4}}$ b $\frac{y^{4}}{x^{3}}$…

which expression is equivalent to $(x^{1/2}y^{-2/3})^{-6}$? a $\frac{x^{3}}{y^{4}}$ b $\frac{y^{4}}{x^{3}}$ c $x^{3}y^{4}$ d $\frac{1}{x^{3}y^{4}}$

which expression is equivalent to $(x^{1/2}y^{-2/3})^{-6}$? a $\frac{x^{3}}{y^{4}}$ b $\frac{y^{4}}{x^{3}}$ c $x^{3}y^{4}$ d $\frac{1}{x^{3}y^{4}}$

Answer

Explanation:

Step1: Apply power - of - a - product rule

$$(x^{1/2}y^{-2/3})^{-6}=(x^{1/2})^{-6}(y^{-2/3})^{-6}$$

Step2: Apply power - of - a - power rule

For $(x^{1/2})^{-6}$, we have $x^{\frac{1}{2}\times(-6)} = x^{-3}$. For $(y^{-2/3})^{-6}$, we have $y^{(-\frac{2}{3})\times(-6)}=y^{4}$. So, $(x^{1/2})^{-6}(y^{-2/3})^{-6}=x^{-3}y^{4}=\frac{y^{4}}{x^{3}}$

Answer:

B. $\frac{y^{4}}{x^{3}}$