Advanced MathHardRewriting an exponential with a different base
Advanced Math practice question
Which expression is equivalent to 8ˣ?
- A. 2³ˣCorrect
- B. 2ˣ⁺³
- C. 4²ˣ
- D. 2ˣ · 3
Answer: A. 2³ˣ
8 is 2³, so 8ˣ = (2³)ˣ. A power raised to a power multiplies the exponents: 2³ˣ.
Why the other answers are wrong
- B. 2ˣ⁺³
- 2ˣ⁺³ is 2ˣ · 2³ = 8 · 2ˣ, which is 8 times 2ˣ — not 8 to the power x. Exponents multiply here, they don't add.
- C. 4²ˣ
- 4²ˣ = (2²)²ˣ = 2⁴ˣ, which is 16ˣ, not 8ˣ.
- D. 2ˣ · 3
- 2ˣ · 3 is three times 2ˣ. The 3 must be an exponent, not a multiplier.
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