Learning powers and roots — exponents
"Powers are shorthand for repeated multiplication: 2⁵ means 2·2·2·2·2. They grow at breathtaking speed — and roots are the way back down. Exponent laws and square numbers carry algebra, units and science."
What is this topic about?
A power aⁿ multiplies a base a by itself n times: 10³ = 10·10·10 = 1000. Square numbers (1, 4, 9, 16, 25 …) are the backbone — areas of squares, the a²/b²/c² of Pythagoras and the x² of quadratics all live here. The exponent laws stay simple: same base multiplied → add exponents (x²·x³ = x⁵), power of a power → multiply them, dividing → subtract. Roots reverse powers: √25 = 5 because 5² = 25; grades 9–10 add negative and fractional exponents (2⁻¹ = 1/2) and powers of ten for scientific notation (3.2 × 10⁴).
The best way to learn it
Memorize the square numbers up to 20² = 400 — they unlock roots, Pythagoras and factoring.
Same base? Add the exponents: x² · x³ = x⁵ — never multiply the bases.
Powers of ten count the zeros: 10⁴ = 10000 — one zero per exponent.
Frequently asked questions
Practise powers in a duel
Igraj sadaPrint powers worksheets
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