How do you simplify #((3^6)^n times (81)^(2n)) / (3^n)^4#?
1 Answer
May 27, 2016
Explanation:
- Simplifying
#81# by prime factorisation (expressing a number as a product of its prime factors):
So,
- Applying below mentioned property to the expression:
#color(blue)(a^m)^n =a ^(mn)# -
# (3^4 )^(2n) = color(green)( 3 ^(8n)# -
#(3^6)^n = 3^(6n)# -
#(3^n)^4 = 3^(4n)#
The expression can now be written as:
- Applying below mentioned property to the numerator:
#color(blue)(a^m xx a^n = a ^(m+n)#
- Applying below mentioned property to the expression:
#color(blue)(a^m / a ^n = a ^(m-n)#