The expression x#y denotes the product of the consecutive multiples of 3 between x and y, inclusive. What is the sum of the exponents in the prime factorization of 21#30?	Choose the correct choice
A) 10 B) 11 C) 12 D) 13 E) 14
First, let's translate the expression 21#30, using the definition given:   21#30 = 21×24×27×30   We need the prime factorization of this product.   Let's factor out 3 from each multiple.   21#30 = 3^4(7×8×9×10)   Now let's replace each consecutive integer with its prime factorization:   21#30 = 3^4(7×2^3×3^2×(2×5))   Let's group the prime bases:   21#30 = 2^4×3^6×5×7   The sum of the exponents is  4 + 6 + 1 + 1= 
<gadget id="calculator"> 4 + 6 + 1 + 1</gadget>
<output>12</output>
12   The answer is 12.
<result>C</result>
The expression x#y denotes the product of the consecutive multiples of 3 between x and y, inclusive. What is the sum of the exponents in the prime factorization of 21#30?