Activities 9

9.1)

Simplify and write as a single power, if possible:

a)

$\frac{\sqrt[10]{2^{-3}}\times \sqrt[5]{2^3}}{\sqrt[5]{2^4}}$

b)

$\frac{\sqrt[3]{4^2}\times {\left(\sqrt[2]{2^3}\right)}^{-1}}{\sqrt[3]{2}\times \sqrt{4}}$

c)

$\frac{\sqrt[3]{3}}{\sqrt[3]{{\left(\frac{1}{3}\right)}^2}}$

9.2)

Simplify and write as a single power if possible:

a)

$\frac{\sqrt[10]{b^3}\cdot \sqrt[5]{b^{-3}}}{\sqrt[5]{b^{-4}}}$

b)

$\frac{\sqrt[3]{a^2}\cdot {\left(\sqrt[2]{b^3}\right)}^{-1}}{\sqrt[3]{a}\cdot \sqrt{b}}$

c)

$\frac{\sqrt[3]{x}}{\sqrt[3]{{\left(\frac{x}{y}\right)}^2}}\cdot \sqrt[3]{{\left(\frac{y^2}{x}\right)}^2}$

You can find the solutions here.