Question 36544
{{{ (8/27)^(-2/3)}}}


When raising a number to a fractional power, the denominator of the exponent ALWAYS gives the index of the radical, and the numberator of the exponent always gives the power that you raise it to.


{{{ (x)^(m/n)}}} means {{{ (root(n,x))^m }}}


In this case, {{{ (8/27)^(-2/3)}}} means {{{ (root(3,(8/27)))^-2}}}


Of course, the cube root of 8 is 2, and the cube root of 27 is 3, so you have:
{{{(2/3)^-2 }}}


Now, when you have a fraction raised to a negative power, it means to invert the fraction.  The fact that it is a -2 power, means you must INVERT the fraction, and SQUARE it.


{{{ (3/2)^2}}}
{{{27/8}}}


R^2 at SCC