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Which of the following statements is true regarding the expression 2^(x+y)?

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Question: Which of the following statements is true regarding the expression 2^(x+y)?

Options:

  1. It can be expressed as 2^x + 2^y.
  2. It can be expressed as 2^x * 2^y.
  3. It is always greater than 1.
  4. It is equal to x + y.

Correct Answer: It can be expressed as 2^x * 2^y.

Solution: 

The property of exponents states that a^(m+n) = a^m * a^n.

Which of the following statements is true regarding the expression 2^(x+y)?

Practice Questions

Q1
Which of the following statements is true regarding the expression 2^(x+y)?
  1. It can be expressed as 2^x + 2^y.
  2. It can be expressed as 2^x * 2^y.
  3. It is always greater than 1.
  4. It is equal to x + y.

Questions & Step-by-Step Solutions

Which of the following statements is true regarding the expression 2^(x+y)?
  • Step 1: Identify the expression given in the question, which is 2^(x+y).
  • Step 2: Recall the property of exponents that states a^(m+n) = a^m * a^n.
  • Step 3: Apply this property to the expression 2^(x+y).
  • Step 4: Rewrite 2^(x+y) using the property: 2^(x+y) = 2^x * 2^y.
  • Step 5: Conclude that the statement 2^(x+y) = 2^x * 2^y is true.
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