Product of Powers

For any number a, and all integers m and n, a^m · aⁿ = a^{m + n}

a² · a⁶ = a^{2 + 6} = a⁸

Power of a Power

For any number a, and all integers m and n, (a^m)ⁿ = a^mn

(a²)⁶ = a^{2 · 6} = a¹²

Power of a Product

For all numbers a and b, and any integer m, (ab)^m = a^mb^m

(pq)⁴ = p⁴q⁴

Power of a Monomial

For all numbers a and b, and all integers m, n and p, (a^mbⁿ)^p = a^mpb^np

(s⁴t)³ = (s⁴ t¹)³
         = s^{4 · 3} t^{1 · 3}
         = s¹² t³