Với $n \in {\mathbb{N}^*}$ thì $a.a.....a$ ($n$ thừa số $a$) được viết gọn lại là:

$a > 0$

$a = 0$

$a \ne 0$

$a < 0$

${a^{\dfrac{3}{2}}} = \sqrt {{a^3}}$          

${a^{\dfrac{3}{2}}} = \sqrt[3]{{{a^2}}}$

${a^{\dfrac{3}{2}}} = \sqrt[6]{a}$

${a^{\dfrac{3}{2}}} = \sqrt[3]{{{a^6}}}$

${a^{\dfrac{1}{{10}}}} = \sqrt[{10}]{a}$

${a^{\dfrac{1}{{10}}}} = \sqrt {{a^{10}}}$

${a^{\dfrac{1}{{10}}}} = {a^{10}}$

${a^{\dfrac{1}{{10}}}} = \sqrt[a]{{10}}$

${a^{545}} = {a^5}.{a^9}$

${a^{45}} = {a^5} + {a^9}$

${a^{45}} = {a^9}:{a^5}$

${a^{45}} = {\left( {{a^9}} \right)^5}$

${\left( {{a^3}} \right)^2} = {a^3}.{a^2}$

${a^3}.{a^2} = {a^6}$

${a^6} = {a^3} + {a^3}$

${\left( {{a^3}} \right)^2} = {\left( {{a^2}} \right)^3}$

${\left( {\sqrt 2  - 1} \right)^2} > 1$

${\left( {\sqrt 2  - 1} \right)^2} = 1$

${\left( {\sqrt 2  - 1} \right)^2} < 1$

${\left( {\sqrt 2  - 1} \right)^2} > 2$