Topic Content:
- Law 2: Division Law
\( \scriptsize a^m \div a^n = a^{m \: – \: n} \)
Similar to the Multiplication Law, the Division Law applies only when we have numbers with the same base numbers.
e.g.
27 ÷ 22
= 27-2
= 25
By expansion:
= \(\scriptsize 2^7 \: \div \:2^2 \\= \frac{2^7}{2^2} \\ = \frac{2 \: \times \: 2 \: \times \: 2\: \times \: 2\: \times \: 2\: \times \: 2\: \times \: 2}{2 \: \times \: 2}\\ = \frac{2 \: \times \: 2 \: \times \: 2\: \times \: 2\: \times \: 2\: \times \: \not{2}\: \times \: \not{2}}{\not{2}\: \times \: \not{2}}\\ \scriptsize = 2^5\)
Worked Example 5.2.1:
Simplify the following by expansion
a. 76 ÷ 72
b. m9 ÷ m4
c. x7 ÷ x4
d. h10 ÷ h4
e. 1312 ÷139
f. 18h5 ÷ 9h4
g. 3x2 ÷ 21x7
Solution
a. \(\scriptsize 7^6 \: \div \:7^2 \\= \frac{7^6}{7^2} \\ = \frac{7 \: \times \: 7 \: \times \: 7\: \times \: 7\: \times \: \not{7}\: \times \: \not{7}}{\not{7} \: \times \: \not{7}}\\ \scriptsize = 7^4\)
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