81-3/4 Can you explain what happens with the negative exponent and what is a rational exponent?

A rational exponent is just a fractional exponent such as 5/4, 3/4 etc.

81 ^(-3/4)   means the same as

 [81^(1/4)]^(-3)  ....  and 81^(1/4)  = 3    ....so we have...

[3]^(-3) =  

1 /3^(3)  =

1/27