Receiving power from antenna (Homework)
You are confusing dB with "linear" units.

To convert from mW (a linear unit) to dBm (decibels with respect to 1mW), use the equation:

Power_dBm = 10*log10(Power_mW)



As a general rule of thumb, you should always be very suspicious if you're ever multiplying two numbers in dB.  Note the following property of logarithms:

log10(uv) = log10(u) + log10(v)     (Note: Log base 10 shown here, but this is true for any base)

This means that if u and v are initially in linear units, and you're multiplying them together, that's equivalent to taking their logarithms and adding them together (or, converting to dB and then adding them together).  Multiplying two numbers in dB has no obvious meaning that translates to linear units.



Ok, back to the original question.  The equation you presented is only valid for linear units.  In this case, your powers (Pr and Pt) are in mW, and your gains (Gt and Gr) are unitless - or, perhaps more precisely, they are mW per mW.  

So, to use the equation correctly, you need to convert any numbers which are given in dB or dBm back to linear units, plug them in to the equation to find Pr, and then convert Pr back to dBm.



As analogsystemsrf pointed out, there is an equivalent version of the Friis formula which uses inputs in dB - note that now the terms are added together, rather than multiplied.