plify each expression below using the properties of integer exponents. Assume \( m= \) ify by numerical substitution. \( \begin{array}{ll}k^{3} * k^{5} & \text { b. } m^{5} * m^{-2}\end{array} \)

1. To simplify \( k^{3} \cdot k^{5} \), we use the property of exponents that states \[ a^{m} \cdot a^{n} = a^{m+n}. \] Thus, \[ k^{3} \cdot k^{5} = k^{3+5} = k^{8}. \] For numerical substitution, if we let \( k=2 \): \[ k^{3} \cdot k^{5} = 2^3 \cdot 2^5 = 8 \cdot 32 = 256, \] and also, \[ k^8 = 2^8 = 256. \] The results match. 2. To simplify \( m^{5} \cdot m^{-2} \), we again use the property of exponents: \[ m^{5} \cdot m^{-2} = m^{5+(-2)} = m^{3}. \] For numerical substitution, if we let \( m=3 \): \[ m^{5} \cdot m^{-2} = 3^5 \cdot 3^{-2} = 243 \cdot \frac{1}{9} = 27, \] and also, \[ m^3 = 3^3 = 27. \] The results are consistent.