20. [tex]\(\sqrt{1 \frac{25}{144}} = \)[/tex]
21. Find three different irrational numbers between the rational numbers [tex]\(\frac{5}{7}\)[/tex] and [tex]\(\frac{9}{11}\)[/tex].
22. Find the decimal expansions of [tex]\(\frac{10}{3}\)[/tex], [tex]\(\frac{7}{8}\)[/tex], and [tex]\(\frac{1}{7}\)[/tex].
23. Show how [tex]\(\sqrt{5}\)[/tex] can be represented on the number line.
24. Locate [tex]\(\sqrt{3}\)[/tex] on the number line.
25. Locate [tex]\(\sqrt{2}\)[/tex] on the number line.
26. Find five rational numbers between [tex]\(\frac{3}{5}\)[/tex] and [tex]\(\frac{4}{5}\)[/tex].
27. Find six rational numbers between 3 and 4.
28. Find the value: [tex]\(\frac{4}{216^{-\frac{2}{3}}} + \frac{1}{256^{-\frac{3}{4}}} + \frac{2}{243^{-\frac{1}{5}}}\)[/tex].
29. Find the value: [tex]\(64^{-\frac{1}{3}}\left(64^{-\frac{1}{3}} - 64^{-\frac{1}{3}}\right)\)[/tex].
30. Prove that: [tex]\(\left(\frac{x^a}{x^a}\right)^{a+b} \times \left(\frac{y^b}{x^c}\right)^{b+c} \times \left(\frac{x^c}{x^c}\right)^{c+a}\)[/tex].
31. If [tex]\(\left(\frac{2}{5}\right)^5 \times \left(\frac{25}{4}\right)^3 = \left(\frac{5}{2}\right)^{3x-2}\)[/tex], then find [tex]\(x\)[/tex].
32. If [tex]\(2^{x-2} \cdot 3^{2x-6} = 36\)[/tex], then find [tex]\(x\)[/tex].
33. Prove that: [tex]\(\frac{x^{a(b-c)}}{x^{b(a-c)}} \div \left(\frac{x^b}{x^a}\right)^c = 1\)[/tex].
34. If [tex]\(a = \frac{\sqrt{5}}{8}\)[/tex] and [tex]\(\frac{8}{a} = b \sqrt{5}\)[/tex], then find [tex]\(b\)[/tex].
35. If [tex]\(125^x = \frac{25^x}{5}\)[/tex], then find the value of [tex]\(x\)[/tex].