Mathematics

Perfect squares and perfect cubes: how to recognise, construct, and take the roots of both, plus the patterns (odd-number sums, units-digit rules, prime factorisation) that tie them together, closing with a bit of number history (varga, ghana, mula) and the Hardy–Ramanujan taxicab-number story.

Exponential notation and the laws of exponents (product, power-of-a-power, division, zero and negative exponents), scientific notation, and the naming systems for very large powers of 10 (lakh/crore/arab and million/billion/trillion), built up through thought experiments comparing linear and exponential growth.