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Surds & Indices

b1x bmx bn……..=bl+m+n……..
am x an = a (m+n).
am / an = a (m-n) , a is not equal to 0
(am) n = a (m * n).
a0 = 1
x-m =1/xm
am+1 =am.a
am*a-n =am-n
am-1 =am*1/a,a(m/n)*(n/m)=a,ax=1, then x=0

If the bases are same then powers are also same i.e if am=an and if a!=1 or 0 then it implies m=p

The last digit of the square of any no. can’t be 2,3,7 or 8.

Any square is of the form either 4k, 4k-1, 4k+1.

Product of any no. of even no.’s is even and any no. of odd no.’s is odd.

The product of any n consecutive natural numbers is divisible by n!.