Which of the following is true for the expression 2^(x+1) / 2^(x-1)? (2023)

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Question: Which of the following is true for the expression 2^(x+1) / 2^(x-1)? (2023)

Options:

Correct Answer: 2^1

Exam Year: 2023

Solution:

Using the property of exponents, we have 2^(x+1 - (x-1)) = 2^(x+1-x+1) = 2^2.

Which of the following is true for the expression 2^(x+1) / 2^(x-1)? (2023)

Which of the following is true for the expression 2^(x+1) / 2^(x-1)? (2023)

Step 1: Identify the expression we need to simplify: 2^(x+1) / 2^(x-1).
Step 2: Recall the property of exponents that states a^m / a^n = a^(m-n).
Step 3: Apply this property to our expression: 2^(x+1) / 2^(x-1) becomes 2^((x+1) - (x-1)).
Step 4: Simplify the exponent: (x+1) - (x-1) = x + 1 - x + 1 = 2.
Step 5: Now we have 2^2, which equals 4.

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