Simplify the following expressions using the properties of exponents.
Please show your work.

Answer:
[tex] {a}^{0} = 1 \\ {a}^{1} \times {a}^{4} = {a}^{4 + 1} = {a}^{5} \\ {4}^{2} = 16\\ \\ = \frac{2}{4 \times {4}^{2} \times {a}^{5} } \\ = \frac{1}{32 {a}^{5} } [/tex]