SOLUTION: how do you solve -27^-2/3

First of all the negative sign is not the sign of 27, for it is
the sign of the entire expression.  The above is equivalent to


The exponent is negative which means that it is the reciprocal
of the expression with an exponent with the positive sign.



Now a fractional power with a 1 numerator is the root of the 
base with the same index.  So let's first write the fractional exponent 2/3
as (1/3)(2)

 

Then we use the law of multiplied exponents as



Go back to the rule that a fractional power with a 1 numerator is the 
root of the base with the same index as the denominator of the 
fractional exponent.



The cube root of 27 is 3, so we have



And since 3 squared is 9, we have



Edwin

You can also do it this way, skipping the "root" part.



Multiply exponents:









Edwin