Expand the given expression (1 + (2)/(3)x)8 using the binomial theorem.

The binomial theorem states that $(1+y)^n = 1 + ny + \frac{n(n-1)}{2!}y^2 + \dots$.
Here, $n=8$ and $y=\frac{2}{3}x$.

$$\left(1 + \frac{2}{3}x\right)^8 = 1 + 8\left(\frac{2}{3}x\right) + \frac{8(8-1)}{2!}\left(\frac{2}{3}x\right)^2 + \dots$$ $$= 1 + \frac{16}{3}x + \frac{8 \times 7}{2}\left(\frac{4}{9}x^2\right) + \dots$$ $$= 1 + \frac{16}{3}x + 28\left(\frac{4}{9}x^2\right) + \dots$$ $$= 1 + \frac{16}{3}x + \frac{112}{9}x^2 + \dots$$

By comparing the coefficients of $x$:

$$\frac{4}{3}a = \frac{16}{3}$$

Multiply both sides by 3:

$$4a = 16$$ $$a = \frac{16}{4}$$ $$a = 4$$

$$\frac{2}{3}b = \frac{112}{9}$$

Multiply both sides by 3:

$$2b = \frac{112}{9} \times 3$$ $$2b = \frac{112}{3}$$

Divide both sides by 2:

$$b = \frac{112}{3 \times 2}$$ $$b = \frac{112}{6}$$

Simplify the fraction:

$$b = \frac{56}{3}$$

The values of the constants are $a=4$ and $b=\frac{56}{3}$.

The final answer is $a=4, b=\frac{56}{3}$.