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The expression 4^(x+1) can be rewritten as?

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Question: The expression 4^(x+1) can be rewritten as?

Options:

  1. 2^(2x+2)
  2. 2^(x+1)
  3. 2^(x+2)
  4. 4^x

Correct Answer: 2^(2x+2)

Solution: 

4^(x+1) = (2^2)^(x+1) = 2^(2(x+1)) = 2^(2x+2).

The expression 4^(x+1) can be rewritten as?

Practice Questions

Q1
The expression 4^(x+1) can be rewritten as?
  1. 2^(2x+2)
  2. 2^(x+1)
  3. 2^(x+2)
  4. 4^x

Questions & Step-by-Step Solutions

The expression 4^(x+1) can be rewritten as?
  • Step 1: Start with the expression 4^(x+1).
  • Step 2: Recognize that 4 can be rewritten as 2^2, so replace 4 with 2^2: (2^2)^(x+1).
  • Step 3: Use the power of a power rule, which says (a^m)^n = a^(m*n). Here, apply it: (2^2)^(x+1) becomes 2^(2*(x+1)).
  • Step 4: Simplify the exponent 2*(x+1) to get 2x + 2: 2^(2x+2).
  • Exponential Properties – Understanding how to manipulate exponents, specifically the power of a power rule.
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