Why does the concept of dimension have basic importance?

If $10 \ g \ cm \ s^{-1} = x \ N \ s$,then the number $x$ is

The potential energy of a particle varies with distance $x$ from a fixed origin as $U = \frac{A\sqrt{x}}{x^2 + B}$,where $A$ and $B$ are dimensional constants. Find the dimensional formula for $A/B$.

Planck's constant $(h)$,speed of light in vacuum $(c)$,and Newton's gravitational constant $(G)$ are three fundamental constants. Which of the following combinations of these has the dimension of length?

Frequency $(n)$ is a function of density $(\rho)$,length $(a)$,and surface tension $(T)$. Then its value is:

Due to an explosion underneath water, a bubble started oscillating. If this oscillation has a time period $T$, which is proportional to $p^\alpha S^\beta E^\gamma$, where $p$ is static pressure, $S$ is the density of water, and $E$ is the total energy of the explosion, determine $\alpha, \beta$, and $\gamma$.