THEORY OF INDICES

THEORY OF INDICES


1.amxan=am+n
2.(am)n=amn
3.am/an=am-n
4.(ab)m=ambm
5.a0=1
6.ax/y=y th root of ax=y√ax
7.a1/p=p th root of a
8.(ab/c)m=ambm/cm
9.a∞=∞
10.a-∞=0

Find the least number with which you multiply 882, so that the product may be
a perfect square.
First find the factors of 882.
882 = 2 × 3 × 3 × 7 × 7
Now, 882 has factors as shown above, ‘3’ repeated twice, ‘7’ repeated twice
and ‘2’ only once. So when one more factor ‘2’ is used, then it becomes a perfect
square.
882 × 2 = (2 × 2) × (3 × 3) × (7 × 7)
The least number required is ‘2’


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