Advanced MathEasy–MediumProduct of two powers with the same base
Advanced Math practice question
If x = 2ᵃ and y = 2ᵇ, which expression is equal to xy?
- A. 2^(a + b)Correct
- B. 2^(ab)
- C. 4^(a + b)
- D. 2ᵃ + 2ᵇ
Answer: A. 2^(a + b)
Multiplying powers of the same base adds the exponents: 2ᵃ · 2ᵇ = 2^(a + b).
Why the other answers are wrong
- B. 2^(ab)
- Exponents multiply when a power is raised to a power, not when two powers are multiplied.
- C. 4^(a + b)
- The base stays 2; it does not become 4.
- D. 2ᵃ + 2ᵇ
- That is x + y, not xy.
More Advanced Math questions
- Easy–Medium
If f(x) = 2x² − 3, what is f(4)? - Easy–Medium
Which expression is equivalent to (2x³)(3x⁴)? - Easy–Medium
What are the solutions to x² − 16 = 0? - Easy–Medium
Which expression is equivalent to (x + 5)²? - Easy–Medium
For x ≠ 0, which expression is equivalent to (x² + 3x) / x? - Easy–Medium
What are the solutions to the equation 2(x − 3)² − 32 = 0 ?
Not affiliated with the College Board. SAT is a trademark of the College Board.