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Exponentiation is a mathematical operation, written as $b^n$, involving two numbers, the base b and the exponent or power n, and pronounced as "b raised to the power of n".

So when I have an equation like $x=3$ and transform it to $x^c=3^c$ I would also call it "Exponentation" or raising both sides of the equation to the power of c.

But what if in contrast I transform $x=3$ to $c^x=c^3$ would that still be called "Exponentation" and if so how would I describe it in words? Raising $c$ by both sides of an equation?

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  • First case mentioned I would call raising both sides to the power of $c$. The second mentioned case is referred to as exponentiating both sides (with base $c$). – Doug Jul 29 '22 at 16:06
  • This seems to be more of an English question than a math question. Since you know the English phrase "$b$ raised to the power of $n$", all you need to know is that preserving the preposition "to" is important to English. So it would be "raising $c$ to both sides of an equation", not "raising $c$ by both sides". – Mark S. Jul 30 '22 at 01:22

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