Topic Content:
- Law 1: Multiplication Law
\( \scriptsize a^m \: \times \: a^n = a^{m \:+ \:n} \)
This law applies only when numbers have the same base number.
Note: 23 and 24 have the same base number, 2, while 54 and 61 do not have the same base number because 5 and 6 are different.
e.g.
23 × 24 = 23+4 = 27 ✅
23 × 34 = 2 × 33+4 ❌ (incorrect)
Worked Example 5.1.1 (Using the Multiplication Law):
Simplify the following
a. 25 × 24
b. c5 × c4
c. a2 × a7
d. 52 × 53 × 54
e. 72 × 72 × 73
Solution
a. 25 × 24
= \( \scriptsize 2^{5\:+\:4} \)
= 29
(same base ‘2’)
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