Basic rules of exponents

There's only a handful of rules to remember about exponents.
I've never seen them named anywhere, so names shown are not "official."
•  b⁰ = 1 ← zero power rule
    note: invalid for b = 0
•  b¹ = b ← identity rule
•  a^m = b^m ⇔ a = b ← equal exponents
•  b^m = bⁿ ⇔ m = n ← equal bases
•  a^m × b^m = (ab)^m ← distributive rule
•  b^m × bⁿ = b^{(m + n)} ← product rule
•  b^m / bⁿ = b^{(m - n)} ← quotient rule
    note: b^-1 = 1/b
•  (b^m)ⁿ = b^(mn) ← power rule
    note: does not apply to b^(mn) which is b^mn
•  ⁿ√(b^m) = b^(m/n) ← root rule
    e.g. √ b = sqrt(b) = b^(1/2)