What is the base of this exponent?

Question

Given the following, what is the value of $ 2b^5 $?

$$ b = 5 $$ $$ 2b^2 $$

I'm confused as to whether the exponent applies to $ 2b $ or just $ b $. Thus, does $ 2b^2 $ equal 50 or 100? What is the rule governing this? Can you provide a source?

Answer 1

If you say $(2b)^2$, then the exponent applies to $2b$. In your case the exponent applies to $b$ only.

Answer 2

In your case, the exponent applies just to $b$ so $2b^2=50$ when $b=5$.