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#27?  Options:
A) 6  B) 7  C) 8  D) 9  E) 10
First, let's translate the expression 21#27, using the definition given:   21#27 = 21×24×27   We need the prime factorization of this product.   Let's factor out 3 from each multiple.   21#27 = 3^3(7×8×9)   Now let's replace each consecutive integer with its prime factorization:   21#27 = 3^3(7×2^3×3^2)   Let's group the prime bases:   21#27 = 2^3×3^5×7   The sum of the exponents is  3 + 5 + 1= 
<gadget id="calculator"> 3 + 5 + 1</gadget>
<output>9</output>
9   The answer is 9.
<result>D</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#27?