# Activities 8

## 8.1)

Simplify as much as possible and write as roots:

a)
${a}^{\frac{2}{3}}×{a}^{\frac{1}{2}}$
b)
${b}^{\frac{3}{5}}×{b}^{\frac{4}{15}}$
c)
${c}^{-\frac{4}{12}}×{c}^{\frac{5}{6}}$
d)
${d}^{\frac{1}{3}}×{d}^{-\frac{2}{7}}$
e)
${e}^{\frac{x}{y}}×{e}^{\frac{4x}{9y}}$
f)
${k}^{\frac{1}{3}}×{k}^{\frac{4}{10}}$

a)
${a}^{\frac{2}{3}}×{a}^{\frac{1}{2}}$
b)
${b}^{\frac{3}{5}}×{b}^{\frac{4}{15}}$
c)
${c}^{-\frac{4}{12}}×{c}^{\frac{5}{6}}$
d)
${d}^{\frac{1}{3}}×{d}^{-\frac{2}{7}}$
e)
${e}^{\frac{x}{y}}×{e}^{\frac{4x}{9y}}$
f)
${k}^{\frac{1}{3}}×{k}^{\frac{4}{10}}$

## 8.2)

Simplify and write as a single power if possible:

a)
$\sqrt[5]{{a}^{2}}×\sqrt{a}×\sqrt[10]{{a}^{21}}$
b)
$\sqrt{a}×\sqrt[3]{a}×\sqrt[6]{{a}^{7}}$
c)
$\sqrt{{4}^{2}}×\sqrt[3]{4}×\sqrt[5]{{4}^{3}}$

You can find the solutions here.