We can simplify expressions involving indices using specific laws. These laws help us work efficiently with large and small numbers.
▸ Product Law — When multiplying two powers with the same base, keep the base and add the indices. This only applies when the bases are identical.
Example: a^m x a^n = a^(m+n). For example, 2^3 x 2^5 = 2^(3+5) = 2^8.
▸ Quotient Law — When dividing two powers with the same base, keep the base and subtract the denominator index from the numerator index.
Example: a^m / a^n = a^(m-n) (where a ≠ 0). For example, 5^7 / 5^3 = 5^(7-3) = 5^4.
★ Real-world — M-Pesa Transactions:
If M-Pesa had 10^9 transactions over 10^3 days, the average transactions per day is 10^9 / 10^3 = 10^(9-3) = 10^6 transactions per day.
Audio narration — reads aloud, works offline
In your own words, summarise the main idea of this lesson.