Indices (exponents) show repeated multiplication; a surd is an irrational root such as √2.
1Laws of indices
aᵐ × aⁿ = aᵐ⁺ⁿ, aᵐ ÷ aⁿ = aᵐ⁻ⁿ, (aᵐ)ⁿ = aᵐⁿ
(ab)ⁿ = aⁿbⁿ, a⁰ = 1, a⁻ⁿ = 1/aⁿ
a^(p/q) = (q-th root of a)ᵖ
2Surds
√(a²b) = a√b
Like surds add: m√a + n√a = (m + n)√a
Rationalise 1/(√a + √b) by multiplying by (√a − √b)