2. Expresa en forma de una sola potencia. a. \( \left(\frac{x}{2}\right)^{\frac{1}{3}} \cdot\left(\frac{x}{2}\right)^{\frac{3}{5}} \) b. \( \left(\frac{-3}{4}\right)^{4} \cdot\left(\frac{-3}{4}\right)^{\frac{-2}{5}} \cdot\left(\frac{-3}{4}\right) \) c. \( \left[(1+\sqrt{2})^{\frac{3}{5}}\right]^{\frac{3}{5}}:(1+\sqrt{2})^{\frac{-1}{2}} \) d. \( \left(\frac{-1}{5}\right)^{-7}:\left(\frac{-1}{5}\right)^{-7} \)

vi) \( x-9 \geq-5 \) is increased by 3

iii. Without expending determinant prove that \( \left|\begin{array}{ccc}\alpha & \beta \gamma & \alpha \beta \gamma \\ \beta & \gamma \alpha & \alpha \beta \gamma \\ \gamma & \alpha \beta & \alpha \beta \gamma\end{array}\right|=\left|\begin{array}{ccc}\alpha & \alpha^{2} & \alpha^{3} \\ \beta & \beta^{2} & \beta^{3} \\ \gamma & \gamma^{2} & \gamma^{3}\end{array}\right| \) v. Prove the identity \( \left\{\left[\begin{array}{ccc}1 & w & w^{2} \\ w & w^{2} & 1 \\ w^{2} & 1 & w\end{array}\right]+\left[\begin{array}{ccc}w & w^{2} & 1 \\ w^{2} & 1 & w \\ w & w^{2} & 1\end{array}\right]\right\}\left[\begin{array}{c}1 \\ w \\ w^{2}\end{array}\right]=\left[\begin{array}{l}0 \\ 0 \\ 0\end{array}\right] \)

Teava le equatiaui parawetriche di \( \left\{\begin{array}{l}x+y+z=1 \\ 2 x-y-z=0\end{array}\right. \)

QS Express each of the following having a ralional denominator: \[ \frac{1}{1+\sqrt{2}+\sqrt{3}} \]

Simplify the expression using the Quotient of Powers Property: \( \frac{x^{5}}{x^{2}} \)