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

1 Answer
Jul 19, 2016

Answer:

#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#