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

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Question: Which of the following is true about 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 2.
  4. It is equal to 2 when x and y are both 0.

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

Solution: 

Using the property of exponents, 2^(x+y) = 2^x * 2^y.

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

Practice Questions

Q1
Which of the following is true about 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 2.
  4. It is equal to 2 when x and y are both 0.

Questions & Step-by-Step Solutions

Which of the following is true about the expression 2^(x+y)?
  • Step 1: Understand that 2^(x+y) means 2 raised to the power of (x+y).
  • Step 2: Recall the property of exponents that states a^(m+n) = a^m * a^n for any base 'a'.
  • Step 3: Apply this property to our expression where 'a' is 2, 'm' is x, and 'n' is y.
  • Step 4: Rewrite 2^(x+y) as 2^x * 2^y using the property of exponents.
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