Advanced MathVery hardRewriting a power in terms of two others
Advanced Math practice question
If 2ᵃ = x and 2ᵇ = y, which of the following is equivalent to 2ᵃ⁺ᵇ⁺¹?
- A. 2xyCorrect
- B. xy + 2
- C. x + y + 2
- D. 2(x + y)
Answer: A. 2xy
2ᵃ⁺ᵇ⁺¹ = 2ᵃ · 2ᵇ · 2¹ = x · y · 2.
Why the other answers are wrong
- B. xy + 2
- Adding exponents multiplies the powers; nothing is added.
- C. x + y + 2
- Adding exponents multiplies the powers; nothing is added.
- D. 2(x + y)
- The powers multiply; they are not summed.
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