Question 1126523
{{{ matrix(3,3, "" , " ", " ", x^(-3/2), " =  ", " 9/4 " , " ", " ", " ") }}} <br>

All-in-one-step, raise both sides to the -2/3's power:
{{{ matrix(3,3, "" , " ", " ", (x^(-3/2))^(-2/3) = x^1 = x, " =  ",  (9/4)^(-2/3) = root(3, (4/9)^2) = root(3, (16/81))  , " ", " ", " ") }}} <br>

<br>
Step-by-step:

Square both sides
{{{ matrix(3,3, "" , " ", " ", x^(-3), " =  ", (9/4)^2  , " ", " ", " ") }}} <br>

Raise each side to the  1/3 (cube root):
{{{ matrix(3,3, "" , " ", " ", x^(-1), " =  ", (9/4)^(2/3)  , " ", " ", " ") }}} <br>

Take reciprocal of each side:
{{{ matrix(3,3, "" , " ", " ", x, " =  ",   (9/4)^(-2/3)  = (4/9)^(2/3)  , " ", " ", " ") }}} <br>

This may be written:
{{{ matrix(3,3, "" , " ", " ", x, " =  ",  root(3, 16/81) , " ", " ", " ") }}}   (approx. 0.582387)<br>