prove that

$\frac{x^{a(b-c)}}{x^{b(a-c)}} \div\left(\frac{x^{b}}{x^{a}}\right)^{c}=1$

Express $0 . \overline{4}$ in the form $\frac{p}{q} ;$ where $p$ and $q$ are integers and $q \neq 0$

Show that $0.1 \overline{6}=\frac{1}{6}$

Insert a rational number and an irrational number between the following:

$\sqrt{2}$ and $\sqrt{3}$

The product $\sqrt[3]{2} \cdot \sqrt[4]{2} \cdot \sqrt[12]{32}$ equals

Find the value

$\frac{4}{(216)^{-\frac{2}{3}}}+\frac{1}{(256)^{-\frac{3}{4}}}+\frac{2}{(243)^{-\frac{1}{5}}}$