Question 231101
solve this equation for x: {{{9x^(2/3)-4x^(-4/3)=0}}} 
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Add 4x^(-4/3) to both sides
{{{9x^(2/3) = 4x^(-4/3)}}} 
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The reciprocal gets rid of the negative exponent
{{{9x^(2/3)}}} = {{{4/(x^(4/3))}}}
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Cube both sides; gets rid of the (1/3) exponent
729x^2 = {{{64/(x^4)}}}
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Find the square root of both sides
27x = {{{8/(x^2)}}}
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multiplied both sides by x^2
27x * x^2 = 8
27x^3 = 8
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Divide both sides by 27
x^3 = {{{8/27}}}
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Find the cube root of both sides
x = +/-{{{2/3}}}; (Both solutions checked out in the original equation) 
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Did this make sense to you?