Question

If a=3 and b=-2,find the values of:

(i) $a^a+b^b\left(ii\right)a^b+b^a\left(iii\right)(a+b{)}^{ab}$

Answer 1

$a=3andb=-2\left(i\right)a^a+b^b=a^3+b^{-2}=(3{)}^3+(-2{)}^{-2}=27+\frac{1}{(-2{)}^2}=27+\frac{1}{-2\times (-2)}=27+\frac{1}{4}=\frac{108+1}{4}=\frac{109}{4}\left(ii\right)a^b+b^a=(3{)}^{-2}+(-2{)}^3=\frac{1}{3^2}+(-2)\times (-2)\times (-2)=\frac{1}{3\times 3}+(-8)=\frac{1}{9}-8=\frac{1-72}{9}=-\frac{71}{9}\left(iii\right)(a+b{)}^{ab}={[3+(-2\left)\right]}^{3\times (-2)}=(3-2{)}^{-6}=(1{)}^{-6}=\frac{1}{(1{)}^6}=\frac{1}{1}=1$