# Activities 9

## 9.1)

Simplify and write as a single power, if possible:

a)
$\frac{\sqrt[10]{{2}^{-3}}×\sqrt[5]{{2}^{3}}}{\sqrt[5]{{2}^{4}}}$
b)
$\frac{\sqrt[3]{{4}^{2}}×\phantom{\rule{-0.17em}{0ex}}{\left(\sqrt[2]{{2}^{3}}\right)}^{-1}}{\sqrt[3]{2}×\sqrt{4}}$
c)
$\frac{\sqrt[3]{3}}{\sqrt[3]{\phantom{\rule{-0.17em}{0ex}}{\left(\frac{1}{3}\right)}^{2}}}$

## 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)
$\frac{\sqrt[3]{{a}^{2}}\cdot \phantom{\rule{-0.17em}{0ex}}{\left(\sqrt[2]{{b}^{3}}\right)}^{-1}}{\sqrt[3]{a}\cdot \sqrt{b}}$
c)
$\frac{\sqrt[3]{x}}{\sqrt[3]{\phantom{\rule{-0.17em}{0ex}}{\left(\frac{x}{y}\right)}^{2}}}\cdot \sqrt[3]{\phantom{\rule{-0.17em}{0ex}}{\left(\frac{{y}^{2}}{x}\right)}^{2}}$

You can find the solutions here.