IS EINSTEIN'S E=MC^2 CORRECT?

This is Einstein's famous equation

E = m * c^2

Let's write it in a slightly different form

E = Const^0 * m^1 * c^2

We already notice a very peculiar feature; only three numbers, 0, 1, and 2, appear as powers in that equation. Does the Universe like only small numbers? Or is this a problem with Einstein's thinking, trying to get things as simple as possible because they are more beautiful that way? There may be an issue.

Let's add units to both sides.

E[kg^1 * (m/s)^2] = m[kg^1] * c[(m/s)^2]

How can this equation be modified? Assume that energy is not a perfect quadratic function of the speed of light. Then, it's obvious that a Const constant needs to be introduced. The constant is non-physical; let's tolerate it for a moment. For example, the Boltzmann and the Avogadro constant are both non-physical.

Let's introduce powers of a, b for the Const, y for the mass, and z for the speed of light.

E[kg^1 * (m/s)^2] = Const[kg^a * (m/s)^b] * m^y[kg^y] * c^z[(m/s)^z]

For units to work, we have those equations.

kg^1 = kg^a * kg^y

1 = a + y

so a = 1 - y

(m/s)^2 = (m/s)^b * (m/s)^z

2 = b + z

so b = 2 - z

The new equation is now.

E[kg^1 * (m/s)^2] = Const[kg^(1 - y) * (m/s)^(2 - z)] * m^y[kg^y] * c^z[(m/s)^z]

Let's assume, as an example, that y=1.02, z=1.97

E[kg^1 * (m/s)^2] = Const[(m/s)^0.03 / kg^0.02] * m^1.02[kg^1.02] * c^1.97[(m/s)^1.97]

Without units, the modified equation looks like that

E = Const * m^1.02 * c^1.97

where units are as follows:

E[kg^1 * (m/s)^2] or E[J], Const[(m/s)^0.03 / kg^0.02], m[kg], and c[m/s]. Only mass and the speed of light effects on energy are affected.

For the second example, y=0.97 and z= 2.04, a weaker effect coming from mass and a more substantial effect coming from the speed of light.

E = Const * m^0.97 * c^2.04

Now we would have E[J], Const[kg^0.03 / (m/s)^0.04], m[kg], and c[m/s].

Could this be true? How to verify if our ideas are correct?

Deviations from the Einstein equation could show up with relatively high energies. Where to find such examples? Perhaps in some stars or nuclear explosions. People familiar with astronomy can identify potential objects with high energies. Then pointing a Webb telescope in that direction may give us some surprises.