How do exponents raised to another exponent work?
1 Answer
Mar 29, 2016
See explanation...
Explanation:
One way of visualising basic positive integer exponents is as repeated multiplication:
#a^n = overbrace(a xx a xx .. xx a)^"n times"#
Then we find:
#a^m xx a^n = overbrace(a xx a xx .. xx a)^"m times" xx overbrace(a xx a xx .. xx a)^"n times"#
#=overbrace(a xx a xx .. xx a)^"m + n times" = a^(m+n)#
The next level of complexity is when a value that has been raised to an exponent is raised to another exponent:
#(a^b)^c = a^(bc)#
For example,
The next level is where a value is raised to a value that has been raised to an exponent:
Note that
So:
#a^(b^c) = a^((b^c))#
For example,