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Okay, let's find the values of the polynomials at the specified points.

(i) p(y) = y2 – y + 1

p(0) = 02 – 0 + 1 = 1

p(1) = 12 – 1 + 1 = 1

p(2) = 22 – 2 + 1 = 3

(ii) p(t) = 2 + t + 2t2 – t3

p(0) = 2 + 0 + 2(0)2 – 03 = 2

p(1) = 2 + 1 + 2(1)2 – 13 = 4

p(2) = 2 + 2 + 2(2)2 – 23 = 4

(iii) p(x) = x3

p(0) = 03 = 0

p(1) = 13 = 1

p(2) = 23 = 8

(iv) p(x) = (x – 1) (x + 1)

p(0) = (0 – 1) (0 + 1) = -1

p(1) = (1 – 1) (1 + 1) = 0

p(2) = (2 – 1) (2 + 1) = 3

Here are the final answers:

(i) p(0) = 1, p(1) = 1, p(2) = 3

(ii) p(0) = 2, p(1) = 4, p(2) = 4

(iii) p(0) = 0, p(1) = 1, p(2) = 8

(iv)

p(0) = -1, p(1) = 0, p(2) = 3

(i) $\dfrac{1}{\sqrt{7}}$:
Multiply numerator and denominator by $\sqrt{7}$:

$$\dfrac{1}{\sqrt{7}} \cdot \dfrac{\sqrt{7}}{\sqrt{7}} = \dfrac{\sqrt{7}}{7}.$$

(ii) $\dfrac{1}{\sqrt{7}-\sqrt{6}}$:
Multiply numerator and denominator by $\sqrt{7}+\sqrt{6}$:

$$\dfrac{1}{\sqrt{7}-\sqrt{6}} \cdot \dfrac{\sqrt{7}+\sqrt{6}}{\sqrt{7}+\sqrt{6}} = \dfrac{\sqrt{7}+\sqrt{6}}{(\sqrt{7})^2-(\sqrt{6})^2}.$$ $$=\frac{\sqrt{7}+\sqrt{6}}{7-6}=\sqrt{7}+\sqrt{6}\mathrm{.}$$

(iii) $\dfrac{1}{\sqrt{5}+\sqrt{2}}$:
Multiply numerator and denominator by $\sqrt{5}-\sqrt{2}$:

$$\dfrac{1}{\sqrt{5}+\sqrt{2}} \cdot \dfrac{\sqrt{5}-\sqrt{2}}{\sqrt{5}-\sqrt{2}} = \dfrac{\sqrt{5}-\sqrt{2}}{(\sqrt{5})^2-(\sqrt{2})^2}.$$ $$= \dfrac{\sqrt{5}-\sqrt{2}}{5-2} = \dfrac{\sqrt{5}-\sqrt{2}}{3}.$$(iv) $\dfrac{1}{\sqrt{7}-2}$:
Multiply numerator and denominator by $\sqrt{7}+2$:

$$\dfrac{1}{\sqrt{7}-2} \cdot \dfrac{\sqrt{7}+2}{\sqrt{7}+2} = \dfrac{\sqrt{7}+2}{(\sqrt{7})^2-(2)^2}.$$ $$= \dfrac{\sqrt{7}+2}{7-4} = \dfrac{\sqrt{7}+2}{3}.$$

1.   9^(3/2)=9^3/2=27/2=13.5                                                                                                    2.   32^(2/5)=32^2/5=64/5 =12.8                                                                                              3.   16^(3/4)=16^3/4=48/4 =12                                                                                                 4.   125^1/3=125/3  =41.6667