Assuming that x, y, z are positive real numbers, simplify each of the

1.	Assuming that x, y, z are positive real numbers, simplify each of the following: (i) (√x−3)5 (ii) √x3y−2 (iii) (x−2/3y−1/2)2 (iv) (√x)−2/3√y4 ÷ √xy−1/2 (v) 5√243x10y5z10 (vi) (x−4y−10)5/4 (vii) (√2√3)5(67)2
Answer» Assuming that x, y, z are positive real numbers, simplify each of the following: (i) ${(\sqrt{x^{- 3}})}^{5}$ (ii) $\sqrt{x^{3} y^{- 2}}$ (iii) $(x^{- 2 / 3} y^{- 1 / 2})^{2}$ (iv) $(\sqrt{x})^{- 2 / 3} \sqrt{y^{4}} \div \sqrt{x y^{- 1 / 2}}$ (v) $5 \sqrt{243 x^{10} y^{5} z^{10}}$ (vi) ${(\frac{x^{- 4}}{y^{- 10}})}^{5 / 4}$ (vii) ${(\frac{\sqrt{2}}{\sqrt{3}})}^{5} {(\frac{6}{7})}^{2}$

Assuming that x, y, z are positive real numbers, simplify each of the following: (i) (√x−3)5 (ii) √x3y−2 (iii) (x−2/3y−1/2)2 (iv) (√x)−2/3√y4 ÷ √xy−1/2 (v) 5√243x10y5z10 (vi) (x−4y−10)5/4 (vii) (√2√3)5(67)2

Answer»

Assuming that x, y, z are positive real numbers, simplify each of the following:

(i) ${(\sqrt{x^{- 3}})}^{5}$

(ii) $\sqrt{x^{3} y^{- 2}}$

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

(iv) $(\sqrt{x})^{- 2 / 3} \sqrt{y^{4}} \div \sqrt{x y^{- 1 / 2}}$

(v) $5 \sqrt{243 x^{10} y^{5} z^{10}}$

(vi) ${(\frac{x^{- 4}}{y^{- 10}})}^{5 / 4}$

(vii) ${(\frac{\sqrt{2}}{\sqrt{3}})}^{5} {(\frac{6}{7})}^{2}$