Answer
$$\left( a \right)\frac{1}{{16}},\,\,\,\,\left( b \right)8,\,\,\,\left( c \right)\frac{1}{3}$$
Work Step by Step
$$\eqalign{
& \left( {\bf{a}} \right)\,\,\,\,{2^{ - 4}} \cr
& {\text{Use the property }}{a^{ - n}} = \frac{1}{{{a^n}}} \cr
& = \frac{1}{{{2^4}}} \cr
& {\text{simplify}} \cr
& = \frac{1}{{16}} \cr
& \cr
& \left( {\bf{b}} \right)\,\,\,\,{4^{1.5}} \cr
& {\text{write 1}}{\text{.5 as }}3/2 \cr
& = {4^{3/2}} \cr
& {\text{Use the property }}{\left( {{a^m}} \right)^n} = {a^{mn}} \cr
& = {\left( {{4^{1/2}}} \right)^3} \cr
& {\text{Use the property }}{a^{m/n}} = \root n \of {{a^m}} \cr
& = {\left( {\sqrt 4 } \right)^3} \cr
& {\text{simplify}} \cr
& = {\left( 2 \right)^3} \cr
& = 8 \cr
& \cr
& \left( {\bf{c}} \right)\,\,\,\,{9^{ - 0.5}} \cr
& {\text{write }} - 0.{\text{5 as }} - 1/2 \cr
& = {9^{ - 1/2}} \cr
& {\text{Use the property }}{a^{ - n}} = \frac{1}{{{a^n}}} \cr
& = \frac{1}{{{9^{1/2}}}} \cr
& {\text{Use the property }}{a^{m/n}} = \root n \of {{a^m}} \cr
& = \frac{1}{{\sqrt 9 }} \cr
& = \frac{1}{3} \cr} $$
