# 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,