A grammar question on taking powers "... we find that
$$ 3x>2x .$$
raising both sides as a power of $2$, we get
$$ 2^{3x}>2^{2x} .$$
So the inequa..."
My question, is the part "raising both sides as a power of $2$" suitable for the formal(I mean in a mathematics book or related materials like articles) mathematical language?
Edit: The way I ask tis question is a little bit confusing I think.
The mathematical equtions between thefirst quatition marks was actually random. What I want was is "raising both sides as a power of $2$" grammatically true? if it is not, then what would you say?
Anyway, your answers are quite helpful for the random question :)
 A: This is more an English-language question than a mathematical question. The phrase "raising both sides as a power of $2$" sounds ungrammatical to me. Indeed, Merriam-Webster does not list "raise as" as a possibility, but it does list the mathematical notion "raise to" (https://www.merriam-webster.com/dictionary/raise).
I would rephrase it as "Exponentiating both sides" (ignoring the base $2$), or even just "Therefore" (trusting that the reader will see that both sides have been exponentiated). I feel that "Exponentiate with base $2$" and similar phrasing is both unnatural and too verbose.
A: The function $f(x)=2^x$ is a strictly increasing function.  Hence, if $y<z$, then $f(y)<f(z)$.  
In the OP, $y=2x$ while $z=3x$.  Note that this holds only for $x>0$.
In therms of the phrasing, it is a bit awkward but correct.  In my view, this phrasing is not significantly worse than other awkward alternatives.
A: *

*"Do $2$ to the power of.... on both sides." (is not correct in terms of grammar, but is most easily understood IMO)

*"Put both sides as a power of $2$"

*"Make $2$ as a base of $2^x$ and $3^x$" (although this might be better for logarithms)

*"Exponentiate with respect to base $2$"

*"Raise both sides in terms of base $2$"
Otherwise, raising both sides to the power $2$ is OK.
A: "Raising both sides as a power of 2" is fine.
Note that the step is correct in this case since $f(x)=2^x$ is a strictly increasing function when $3x>2x$ that is $x>0$.
