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

2 Answers
Nov 11, 2016

(81)/(16b^12)

Explanation:

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)

Nov 11, 2016

81/(16b^12)

Explanation:

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)