Looking Back

(1) Very large numbers are easier to read, write and understand when expressed in form.

(2) 10,000 = 104 (10 raised to the power of 4); 243 = 35 (3 raised to the power of 5); 64 = 26 (2 raised to the power of 6). In these examples 10, 3, 2 are the respective and 4, 5, 6 are the respective .

(3) Laws of Exponents: For any non-zero integers 'a' and 'b' and integers 'm' and 'n':

(i) am × an = am+nam−n

(ii) amn = amnamn

(iii) am × bm = abmab1m

(iv) a−n = 1an −1an

(v) aman = am−nam+n if m > n

(vi) aman = 1am−nam−n if n > m

(vii) abm = ambmbmam

(viii) a0 = (where a ≠ 0)