Apply all relevant properties of exponents to simplify the following expressions. Enter your answer as an integer or completely simplified fraction without negative exponents. a) \( r^{-7} r^{4} \) Answer b) \( p^{3} p^{-9} \) Answer c) \( t^{-5} t^{8} \) Answer d) \( q^{4} q^{-9} q^{-7} \) Answer

To simplify the expressions using the properties of exponents, we can apply the rule that states \(a^m \cdot a^n = a^{m+n}\). a) \( r^{-7} r^{4} = r^{-7 + 4} = r^{-3} = \frac{1}{r^{3}} \) b) \( p^{3} p^{-9} = p^{3 - 9} = p^{-6} = \frac{1}{p^{6}} \) c) \( t^{-5} t^{8} = t^{-5 + 8} = t^{3} \) d) \( q^{4} q^{-9} q^{-7} = q^{4 - 9 - 7} = q^{-12} = \frac{1}{q^{12}} \)