How do you simplify #((16n ^(2/3))/(81n ^(-2/3))) ^(-3/4)#?

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Answer 1 · 2016-06-12T17:18:23

#((16n^(2/3))/(81n^(-2/3)))^(-3/4)=27/(8n)#

#((16n^(2/3))/(81n^(-2/3)))^(-3/4)#

= #((2^4n^(2/3))/(3^4n^(-2/3)))^(-3/4)#

= #(((2^4)^(-3/4)(n^(2/3))^(-3/4))/((3^4)^(-3/4)(n^(-2/3))^(-3/4)))#

= #((2^((4xx-3/4))n^((2/3xx(-3/4))))/(3^(4xx(-3/4))n^((-2/3)xx(-3/4))))#

= #((2^(-3)n^(-1/2)))/(3^(-3)n^(1/2))#

= #((3^3n^(-1/2)))/(2^3n^(1/2))#

= #27/(8n)#