The expression 65 √35x45. 8√28x is equivalent to axb, where a and b are positive constants and x > 1. What is the value of a + b?
Correct answer: C. 361/8
- A. 40
- B. 60
- C. 361/8
- D. 10
Explanation
The given expression is 65√35x45. 8√28x. To simplify, apply the properties of exponents and roots:Recognize that √35 is the same as (35)^(1/2) = 35/2.The expression becomes 65 * 35/2 * 45 * 28/2 * x1. Simplify further:Combine the exponents for common bases, and simplify the expression using properties of exponents: (6 * 4)5 * 35/2 * 24 * x.Calculate the coefficients: (24)5 = 65 * 45.Combine all terms to get a = 361/8 and b = 1. Thus, a + b = 361/8 + 1 = 369/8.Hence, the answer is 361/8. Other options result from incorrect simplification steps or arithmetic errors.
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