How do you simplify #3^5*3^4#?

1 Answer
sente
Feb 13, 2016

#3^5*3^4=3^9#

Explanation:

Using the property #a^n*a^m=a^(n+m)#:

#3^5*3^4=3^(5+4)=3^9#

To gain some intuition as to why this property works, let's try expanding the exponent into multiplication:

#a^n*a^m=(a*a*a*...*a)(a*a*a*...*a)# where the first parentheses contain #n# #a#'s and the second parentheses contain
#m# #a#'s. Thus, there are #n+m# total #a#'s being multiplied, or #a^(n+m)#

The above is a simple way of seeing why this property works for positive integer exponents, however the property does hold for all exponents (including negative numbers, fractions, irrational numbers, and so on).

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