▸ Power of a Power Law — When raising a power to another power, multiply the indices.
Example: (a^m)^n = a^(m*n). For example, (3^2)^4 = 3^(2*4) = 3^8.
▸ Zero Index Law — Any non-zero number raised to the power of zero equals 1.
Example: a^0 = 1 (where a ≠ 0). For example, 15^0 = 1.
▸ Negative Index Law — A negative index means the reciprocal of the positive index.
Example: a^(-n) = 1 / a^n (where a ≠ 0). For example, 2^(-4) = 1 / 2^4 = 1/16.
★ Real-world — Medicine Half-Life:
The half-life of a drug models exponential decay. If a drug concentration halves every 4 hours, after t hours, the concentration A can be modeled as A = C * 2^(-t/4), where C is the initial concentration. Negative indices are crucial here.
Audio narration — reads aloud, works offline
In your own words, summarise the main idea of this lesson.