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a) $2^{5}$ = 2*2*2*2*2 = 32;

b) $(- 5)^{3}$ = (-5)*(-5)*(-5) = -125;

c) ${0.4}^{3}$ = 0.4*0.4*0.4 = 0.064;

d) $(- 0.4)^{3}$ = (-0.4)*(-0.4)*(-0.4) = -0.064;

e) $(\frac{1}{2})^{5}$ = $\frac{1}{2}$ * $\frac{1}{2}$ = $\frac{1}{32}$

g) $(\frac{- 1}{3})^{4}$ = $\frac{- 1}{3}$ * $\frac{- 1}{3}$ * $\frac{- 1}{3}$ * $\frac{- 1}{3}$ = $\frac{1}{81}$

h) ${21.5}^{0}$ = 1

i) $(3 \frac{1}{2})^{2}$ = $(\frac{7}{2})^{2}$ = $\frac{7}{2}$ * $\frac{7}{2}$ = $\frac{49}{4}$