16Hit 1600
Advanced MathVery hardCollapsing a sum of equal powers

Advanced Math practice question

For every value of x, the sum 2ˣ + 2ˣ + 2ˣ + 2ˣ is equivalent to 2ˣ⁺ᵏ. What is the value of k?

Answer: 2

Four copies of 2ˣ make 4 · 2ˣ = 2² · 2ˣ = 2ˣ⁺².

Common wrong answers

If you answered 1
Doubling raises the exponent by 1; quadrupling raises it by 2.
If you answered 3
4 = 2²; adding exponents gives x + 2.
If you answered 4
The four copies contribute a factor of 4 = 2², so the exponent rises by 2, not 4.

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