SOLUTION: please help me solve this equation: {{{(343/512)^(-2/3)}}}

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Question 759346: please help me solve this equation: %28343%2F512%29%5E%28-2%2F3%29
Answer by josgarithmetic(39620) About Me  (Show Source):
You can put this solution on YOUR website!
%28343%2F512%29%5E%28-2%2F3%29
=...
=%28512%2F343%29%5E%282%2F3%29=%282%5E9%2F7%5E3%29%5E%282%2F3%29

=%282%5E9%29%5E%282%2F3%29%2F%287%5E3%29%5E%282%2F3%29
=%282%5E3%29%5E2%2F7%5E2
You'll need to finish this, but the steps shown should make the process leading up to here understandable.