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To multiply these expressions, we add the exponents of the common base, which in this case is b and c.
For b, we add the exponents 12 and 7:
b^12 * b^7 = b^(12+7) = b^19
For c, we add the exponents 3 and 1:
c^3 * c = c^(3+1) = c^4
So, the simplified expression is b^19 * c^4.