How do you simplify #(\frac { a ^ { 2} b ^ { 5} } { a ^ { 4} b ^ { 2} } ) ^ { 4}#?

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Answer 1 · 2018-03-24T15:06:54

#=> b^12/a^8#

We start with:

#=>((a^2b^5)/(a^4b^2))^4#

Let's distribute the power of #4#.

#=>(a^((2xx4))b^((5xx4)))/(a^((4xx4))b^((2xx4)))#

#=>(a^(8)b^(20))/(a^(16)b^(8))#

Now we identify like-terms. Powers are subtracted when terms are divided.

#=>a^((8-16))b^((20-8))#

#=>a^(-8)b^(12)#

#=> b^12/a^8#