If `a=2` and `b=3,` then find the values of each of the following: `a^a+b^b` (ii) `a^b+b^a` (iii) `a^b` (iv)`(a/b)^a` (v) `(1/a+1/b)^a`

Explanation

(i) `a^a+b^b=2^2+3^3=2xx2+3xx3xx3=4+27=31`

(ii) `a^b+b^a=2^3+3^2=2xx2xx2+3xx3=8+9=17`

(iii) `a^b=2^3=2xx2xx2=8`

(iv) `(a/b)^a=(2/3)^2=2^2/3^2=(2xx2)/(3xx3)=4/9`

(v) `(1/a+1/b)^a=(1/2+1/3)^2=((3+2)/6)^2=(5/6)^2=5^2/6^2=(5xx5)/(6xx6)=25/36`