5^w * 5^-3w = 1/125
when the base is the same we add the exponents
a faction is a negative exponent
5^(w-3w) = 125^-1
a power to a power is multiplied
5^-2w = (5^3)^-1
5^-2w = 5^ -3
since the bases are the same the exponents are equal
-2w = -3
divide by -2
w = 3/2
8^b-1 * 8^4b = 8^3b
since the bases are the same add the exponents
8^(b-1+4b) = 8^3b
8^(5b-1) = 8^3b
since the bases are the same the exponents must be the same
5b-1 = 3b
subtract 5b from each side
-1 = -2b
divide by -2
1/2 =b
