Question

If the expression 1/2x was placed in the form axᵇ where a and b are real numbers, then which of the following is equal to a+b ? Show how you arrived at your answer.

(A) 1
(B) 1/2
(C) 3/2
(D) - 1/2

Answer 1

The correct answer is (C) 3/2. The expression ½x is equivalent to 0.5x¹, giving us 'a' as 0.5 and 'b' as 1. Thus, a+b equals 1.5 or 3/2.

Step-by-step explanation:

To transform the expression ½x into the form axᵇ, we need to understand that the coefficient 'a' in 'axᵇ' corresponds to the constant term in front of the variable x, while 'b' represents the exponent on x. In our case, the expression already has a coefficient of ½, which is our 'a'. The variable x is to the power of 1 (since any variable without an explicit exponent has an exponent of 1), which is our 'b'. Using these values:

• 'a' is ½, or 0.5.
• 'b' is 1 because x can be written as x¹.

We simply add 'a' and 'b' to get the value of a+b. So, 0.5 + 1 gives us 1.5 or ¾.

Therefore, the correct option is (C) 3/2.