Consider the equation $$H = \frac{x^p \epsilon^q E^r}{t^s}$$
Where $$H$$ = magnetic field; $$E$$ = electric field, $$\epsilon$$ = permittivity, $$x$$ = distance, $$t$$ = time. The values of $$p, q, r$$ and $$s$$ respectively are :

Given:

$$H=(x^pε^qE^r)/t^s$$

step 1: dimensions

$$H(magnetic\ field)=A/m=AL⁻^1$$

$$E(electric\ field)=V/m=MLT⁻^3A⁻^1$$

$$ε(permittivity)=M⁻^1L⁻^3T⁴A^2$$

x = L
t = T

step 2: write RHS dimensions

$$x^p→L^p$$

$$E^r→M^rL^rT^{-3r}A^{-r}$$

$$t^s→T^s(in\ deno\min ator→T⁻s)$$

combine:

M: −q + r
L: p − 3q + r
T: 4q − 3r − s
A: 2q − r

step 3: equate with $$H=AL⁻^1$$

$$M⁰L⁻^1T⁰A^1$$

equations:

−q + r = 0 ⇒ r = q

p − 3q + r = −1 ⇒ p − 2q = −1

4q − 3r − s = 0 ⇒ q − s = 0 ⇒ s = q

2q − r = 1 ⇒ q = 1

step 4: find others

q = 1 ⇒ r = 1, s = 1

p − 2 = −1 ⇒ p = 1