Simplify the expression to a form in which 2 is raised to a single integer power. \( \frac{\left(2^{5}\right)^{3} 2^{-7}}{2^{-6}} \) a.) \( 2^{8} \) b.) \( 2^{15} \) c.) \( 2^{9} \) d.) \( 2^{14} \)

Let's simplify the expression step by step: 1. Start with the expression: \[ \frac{\left(2^{5}\right)^{3} 2^{-7}}{2^{-6}} \] 2. Use the power of a power property, \((a^m)^n = a^{m \cdot n}\): \[ \left(2^{5}\right)^{3} = 2^{15} \] Now, the expression becomes: \[ \frac{2^{15} \cdot 2^{-7}}{2^{-6}} \] 3. Combine the powers in the numerator: \[ 2^{15} \cdot 2^{-7} = 2^{15 - 7} = 2^{8} \] So now we have: \[ \frac{2^{8}}{2^{-6}} \] 4. Apply the property \(\frac{a^m}{a^n} = a^{m - n}\): \[ \frac{2^{8}}{2^{-6}} = 2^{8 - (-6)} = 2^{8 + 6} = 2^{14} \] Thus, the simplified form of the expression is \(2^{14}\). The correct option is: d.) \(2^{14}\)