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

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Answer 1 · 2016-06-12T17:18:23

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

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

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

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

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

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

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

= $27/(8n)$

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