Simplify each expression and eliminate any negative exponents. (a) \( a^{7} a^{8} \) (b) \( \left(-2 b^{-7}\right)^{3} \) (c) \( -2 y^{16} y^{-17} \)

Let's simplify each expression step by step and get rid of any negative exponents. (a) \( a^{7} a^{8} \) To simplify, we can use the property of exponents that states \( a^{m} a^{n} = a^{m+n} \). Therefore, \[ a^{7} a^{8} = a^{7+8} = a^{15}. \] (b) \( \left(-2 b^{-7}\right)^{3} \) Using the power of a product rule, we distribute the exponent over both terms: \[ \left(-2\right)^{3} \cdot \left(b^{-7}\right)^{3} = -8 b^{-21}. \] Now, to eliminate the negative exponent, we recall that \( b^{-n} = \frac{1}{b^{n}} \): \[ -8 b^{-21} = -\frac{8}{b^{21}}. \] (c) \( -2 y^{16} y^{-17} \) We combine the exponents of \( y \) using the same property as before: \[ y^{16} y^{-17} = y^{16 - 17} = y^{-1}. \] Now to eliminate the negative exponent: \[ -2 y^{-1} = -\frac{2}{y}. \] In summary, the simplified expressions are: (a) \( a^{15} \) (b) \( -\frac{8}{b^{21}} \) (c) \( -\frac{2}{y} \)