Answer: [tex]c = \left(\frac{E}{m}\right)^{1/2}[/tex]
This is (E/m) all to the 1/2 power
=================================================
Work Shown:
[tex]E = mc^2\\\\mc^2 = E\\\\c^2 = \frac{E}{m}\\\\c = \left(\frac{E}{m}\right)^{1/2}\\\\[/tex]
The idea is to first isolate [tex]c^2[/tex] by dividing both sides by m. This undoes the multiplication of m and [tex]c^2[/tex]
The next step is to fully isolate c. One way is to apply the square root. Another way is to raise both sides to the 1/2 power. Either way, that will get c all by itself.
Side note: [tex]\sqrt{x} = x^{1/2}[/tex]
So this means that [tex]\left(\frac{E}{m}\right)^{1/2} = \sqrt{\frac{E}{m}}[/tex]
A rational exponent is the same as a fractional exponent.
