indices are the little floating number thingies $$4^{2}$$ (the 2 here). called powers or the index number. the plural of index is indices!!
–> $$x^{m}$$ · $$x^{n}$$ = $$x^{m + n}$$
–> $$x^{0}$$ = 1
–> $$x^{m}$$ ÷ $$x^{n}$$ = $$x^{m - n}$$
–> $$x^{-m}=\:\frac{1}{x^m}$$
–> $$\left(x^m\right)^n=\:x^{mn}$$
–> $$x^{\frac{m}{n}}=\:\left(\sqrt[n]{x}\right)^m$$
examples:
simplify this expression: $$\left(3x^4y^3\right)^2$$ –> $$9x^8y^6$$
simplify this expression: $$\left(x^3\right)^4\div \left(x^6\right)^2$$ –> $$x^{12}\div x^{12}$$ = 1
simplify this expression: $$\left(\frac{x^{2\:}}{\:y}\right)^0$$ = 1