I have read that, if $$b=a\times a\times a\times \cdots \times a \text{ ($n$ times})$$ then $$b=a^n$$ where $b$ is known as the base, $n$ as the index or exponent and $b$ is the power.
The author in many places refers to both $b$ and $n$ as powers. Is this correct? Is there any difference between exponent, index and power?
[Math] the difference between exponent, power and index
exponentiationterminology
Best Answer
Unfortunately, terminologies here can be confusing. I would call $n$ the "exponent". But one might speak of $b$ as "$a$ to the power $n$" (which makes it sound like $n$ is the "power"), or "the $n$'th power of $a$" (which makes it sound like $b$ is the "power").