Assuming that x, y, z are positive real numbers, simplify :
$\sqrt{x^{- 2} y^{3}}$

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Solution

$\sqrt{x^{- 2} y^{3}} = \sqrt{\frac{y^{3}}{x^{2}}}$

$= (\frac{y^{3}}{x^{2}})^{1 / 2}$

$= \frac{y^{3 / 2}}{x}$

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

x + y + z = a

\sqrt{x^{- 1} y} \times \sqrt{y^{- 1} z} \times \sqrt{z^{- 1} x} = 1

x + y + z = 3

\frac{1}{x} + \frac{1}{y} + \frac{1}{z}

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