If an equation is given, state what property of real numbers the equation represents. If an expression is given, write an equivalent expression using properties of exponents or radicals.
\[a+b=b+a\]
\[a\cdot b=b\cdot a\]
\[a\cdot(b\cdot c)=(a\cdot b)\cdot c\]
\[(a+b)+c=a+(b+c)\]
\[a+0=a\]
\[a\cdot 1= a\]
\[a\cdot\frac{1}{a}=1, \quad a\neq0\]
\[a+(-a)=0\]
\[a(b+c)=ab+ac\]
\[a\cdot0=0\]
\[2\cdot3\cdot4= (2\cdot3)\cdot4 \]
\[a^n\cdot a^m\]
\[\dfrac{a^n}{a^m}\]
\[(a^n)^m\]
\[(a\cdot b)^n\]
\[a^{-n}\]
\[a^0\]
\[\biggr(\dfrac{a}{b}\biggr)^n\]
\[a^n\cdot b^n\]
\[\dfrac{a^n}{b^n}\]
\[\biggr(\dfrac{a}{b}\biggr)^{-n}\]
\[\dfrac{a^{-m}}{b^{-n}}\]
\[a^{n/d}\]
\[\sqrt[n]{a}\cdot\sqrt[n]{b}\]
\[\frac{\sqrt[n]{a}}{\sqrt[n]{b}}\]
\[\sqrt[m]{\sqrt[n]{a}}\]
\[\sqrt[n]{a^n} \qquad \text{ assume } n \text{ is odd}\]
\[\sqrt[n]{a^n} \qquad \text{ assume } n \text{ is even}\]
Professor Tim Busken