THE SQUARE OF 50p^16q^8 means

(50p16q8)2 

Give the 50 a 1 exponent so that every factor inside
the parentheses will have an exponent showing.

(501p16q8)2

The 2 is called the OUTSIDE exponent, since it's outside the 
parentheses.  The 1, the 16 and the 8 are called the
INSIDE exponents, because they are inside the parentheses.

Next, remove the parentheses by multiplying each INSIDE
exponent by the OUTSIDE exponent:

501×2p16×2q8×2

502p32q16

Now since 502 means 50×50 or 2500, the final answer is

2500p32q16

Edwin
AnlytcPhil@aol.com