Basic law of exponents are :
i) $a^m.a^n$ = $a^{m+n}$
ii) ($a^m)^n$ = $a^{mn}$
iii) $a^m/a^n$ = $a^(m-n)$ , $m>n$
iv) $a^mb^m$ = $(ab)^m$
v) $a^0$ = 1
vi) ⁿ$√a$ = $a^{1/n}$

Let $a>0$ be a real number. Let $m$ & $n$ be integers such that $m$ and $n$ have no common factors other than 1 (i.e $m$ & $n$ are co-prime ) and $n$>0 . Then
$a^{m/n}$ = ⁿ$√a^m$
We now have following extended laws of exponents
Let $a>0$ be a real number and $p$ and $q$ be rational numbers ,then
i) $a^p.a^q$ = $a^(p+q)$
ii) $(a^p)^q$= $a^{pq}$
iii) $a^p/a^q$ = $a^{p-q}$
iv) $a^p.b^p$ = $(ab)^p$
Simplify (i) $2^{2/3}. 2^{1/3}$
(ii) $(3^{1/5})^4$