Question

If a = 2 and b = 3, then find the values of each of the following:
(i) (a + b)^a
(ii) (ab)^b
(iii) ${\left(\frac{b}{a}\right)}^b$
(iv) ${\left(\frac{a}{b}+\frac{b}{a}\right)}^a$

Answer 1

We have a = 2 and b = 3.
Thus,
(i) (a + b)^a = (2 + 3)² = (5)² = 25

(ii) (ab)^b = (2 x 3 )³ = (6)³ = 216

(iii) ${\left(\frac{b}{a}\right)}^b={\left(\frac{3}{2}\right)}^3=\frac{3}{2}\times \frac{3}{2}\times \frac{3}{2}=\frac{27}{8}$

(iv) ${\left(\frac{a}{b}+\frac{b}{a}\right)}^a={\left(\frac{2}{3}+\frac{3}{2}\right)}^2={\left(\frac{4+9}{6}\right)}^2={\left(\frac{13}{6}\right)}^2=\frac{169}{36}$