a) \( 10^{9} \cdot 10^{(-4)}= \) b) \( \left(-8^{5}\right) \cdot(-8) \cdot\left(-8^{(-4)}=\right. \) c) \( \frac{13}{13^{17}}= \)

For a), when multiplying powers of the same base, you add the exponents. This gives us: \( 10^{9} \cdot 10^{(-4)} = 10^{(9 + (-4))} = 10^{5} \). For b), applying the power rules and remembering that multiplying with the same base involves adding exponents: \(-8^{5} \cdot (-8) \cdot (-8^{-4}) = -8^{(5 + 1 - 4)} = -8^{2} = -64\). For c), using the properties of exponents, \( \frac{13}{13^{17}} = 13^{(1 - 17)} = 13^{-16} \), which can also be expressed as \( \frac{1}{13^{16}} \).