Compare two percentage changes
Starting from 100%, a discount of 20% leaves 80%. Increasing 20% over 80 recovers 100? Calculate before checking: 80 × 1,2 = 96.
Your mission: explain the rules and their limits
Review the operations and proportions in the previous track. Here, start with negative exponent, explore roots and end with models and restrictions.
Rooting makes a bridge to the real: the root of a rational is not always rational. For example, √(9/16) = 3/4 is rational, while √2 is irrational.
Inverse challenge
Calculate (2/3)⁻². Why can’t we use the same zero-based rule?
Check the justification
(2/3)⁻² = (3/2)² = 9/4. Negative integer exponents involve the inverse of the base, which must be nonzero.
To conclude: give a rational and an irrational root of rational numbers, justifying the difference.