Key property: \(\frac{1}{x^n} = x^{-n}\)
For example, \(\frac{1}{5^8} = 5^{-8}\)


So, we can rewrite our sum as follows: \(2^{-10} + 2^{-11} + 2^{-12} + 2^{-12}\)

Factor out \(2^{-12}\) to get: \(2^{-12}(2^2 + 2^1 + 1 + 1)\)

Evaluate to get: \(2^{-12}(4 + 2 + 1 + 1)\)

Simplify: \(2^{-12}(8)\)

Rewrite as follows: \((2^{-12})(2^3)\)

Apply the product law to get: \(2^{-9}\)

Rewrite as: \(\frac{1}{2^{9}}\)

Answer: C

Cheers,
Brent