Question

How do you simplify and write `b^8(2b)^4` with positive exponents?

Answer 1

`b^8(2b)^4=16b^12`

Explanation:

You can look at it this way, in case you ever want to come up with your own formulas:
`(2b)^4=2b*2b*2b*2b=16b^4`
Or more generally, `(ab)^n=a^nb^n`
Next,
`(b^8)(b^4)=(b*b*b*b*b*b*b*b)(b*b*b*b)`
By associativity, we now have:
`b^12`
Hence, more generally, we have `a^m*a^n=a^(m+n)`
Thus, we get `b^8(2b)^4=16b^12`