How do you simplify #(\frac { ( 3b ^ { 2} ) ^ { 2} } { ( b ^ { 2} \cdot 2b ^ { 3} ) ^ { 2} } ) ^ { 2} #?

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Answer 1 · 2016-11-11T14:59:20

#(81)/(16b^12)#

First, according to PEMDAS, simplify what is in the parentheses:
#[[(3b^2)^2]/[(b^2*2b^3)^2]]^2#
#=[[(3b^2)^2]/[(2b^5)^2]]^2#

Now I'll distribute the outermost power to each side of the fraction. Remember the exponent rule that: #(a^b)^c = a^(bc)#

#[(3b^2)^4]/[(2b^5)^4]#

Now, distribute the exponents on each side of the fraction
#(81b^8)/(16b^20)#
Simplify:

#(81)/(16b^12)#

Answer 2 · 2016-11-11T15:42:27

#81/(16b^12)#

There is so much going on inside the brackets, it seems like a good idea to simplify inside the bracket first.

The index outside can be attended to later.

#(color(blue)((3b^2)^2)/(color(red)(b^2xx2b^3))^2)^2#

#=(color(blue)(9b^4)/(color(red)(2b^5))^2)^2#

#=((9b^4)/(4b^10))^2#

#= (9/(4b^6))^2#

#=81/(16b^12)#