Rule 
Reason 
n^{a}
•
n^{b}= n^{a+b} 
n^{2}
•
n^{3}=
nn •
nnn = nnnnn =
n^{5} 
a^{n}
•
b^{n}= (ab)^{n} 
a^{2}
•
b^{2}= aa • bb = (ab)•(ab) = (ab)^{2} 
(n^{b})^{c}
= n^{b+c} 
(n^{3})^{2}
=
(nnn)^{2} = (nnn)•(nnn) = (n^{6}) 

Since a^{b}/a^{b} = 1 then anything multiplied
by one make no difference to the value. Multiply the terms to get a^{b}


( 
a 
) 
2 
=

aa 
=

a^{2} 
b 

bb 
b^{2} 

a
 b = c
b  a = c 
This
is because you can multiply both sides by 1
(1)(a  b) = (1)c
a + b = c
b  a = c 

again, since n/n = 1 then anything
multiplied
by one make no difference to the value. Now multiply out the terms

n(a + b) = an + bn  2(a + b) = (a + b) + (a + b) = a + a + b + b = 2a + 2b 
log(ab) = log(a) + log(b)  This rule is used below 
log(a^{n}) = n•log(a)  log(a^{2}) = log(aa) = log(a) + log(a) = 2•log(a) 