Question

Simplify : $\frac{(\sqrt{x}{)}^{\frac{3}{5}}\times (\sqrt{x}{)}^{\frac{2}{5}}+2\sqrt{x}}{2\left(\right(\sqrt{x}{)}^{\frac{2}{3}}\times \left(\sqrt{x}{)}^{\frac{1}{3}}\right)+\sqrt{x}}$.
(choose two correct alternatives)

• A. $(\sqrt{x}{)}^0$
• B. $1$
• C. $(\sqrt{x}{)}^1$
• D. $3\sqrt{x}$

Answer 1

Answer: (A), (B)

The correct options are
A $(\sqrt{x}{)}^0$
B $1$

$I=\frac{(\sqrt{x}{)}^{\frac{3}{5}}\times (\sqrt{x}{)}^{\frac{2}{5}}+2\sqrt{x}}{2(\sqrt{x}{)}^{\frac{2}{3}}\times (\sqrt{x}{)}^{\frac{1}{3}}+\sqrt{x}}$

$\Rightarrow \frac{(\sqrt{x}{)}^{\frac{2}{5}+\frac{2}{5}}+\sqrt{x}\times 2}{2\times (\sqrt{x}{)}^{\frac{2}{3}+\frac{1}{3}}+\sqrt{x}}\Rightarrow \frac{\sqrt{x}+2\sqrt{x}}{2\sqrt{x}+\sqrt{x}}\Rightarrow \frac{3\sqrt{x}}{3\sqrt{x}}\Rightarrow 1$

$I=1=(\sqrt{x}{)}^0$