2014 AMC 10B Problem 2

Attempt Problem 2 of the 2014 AMC 10B below, then check your answer against the professionally curated solution from LIVE by Po-Shen Loh. You can also try the full timed exam, view all 2014 AMC 10B solutions, or check the answer key.

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2.

What is

\dfrac{2^3 + 2^3}{2^{-3} + 2^{-3}}?

16

24

32

48

64

Answer: E

Concepts:exponent

Difficulty rating: 870

Small hint:

Factor the common

2

from the numerator and denominator

Big hint:

Dividing powers of

2

means subtracting exponents

Solution:

\begin{aligned} \dfrac{2^3 + 2^3}{2^{-3} + 2^{-3}} &= \dfrac{2\cdot 2^3}{2\cdot 2^{-3}} \\&=2^6 \\&= 64 \end{aligned}

Thus, the correct answer is E .