2^10 + 2^10 is equal to which of the following?
- A2^20
- B2^11
- C4^10
- D2^100
- E4^20
Factor before you add exponents
Try it before you scroll. Two minutes on the clock, then commit to an answer.
Correct answer: B
You cannot add exponents here because the rule a^m × a^n = a^(m+n) applies to multiplication, not addition. Instead, factor:
2^10 + 2^10 = 2 × (2^10) = 2^1 × 2^10 = 2^11.
The trap answers map to the most common misapplications:
- (A), 2^20, treats the sum like a product and adds the exponents.
- (D), 2^100, multiplies the exponents.
- (C) and (E) confuse doubling the base with doubling the value: 2^10 + 2^10 is two copies of 2^10, which is 2^11, not 4^10 (that would be (2^2)^10 = 2^20).
Same move in general: a^n + a^n = 2·a^n, and k copies of a^n sum to k·a^n. When k is itself a power of the base, the sum collapses into a single clean power.