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CAPITULO XXX

TEORIA DE LOS EXPONENTES
Ejercicio 220
1. $\frac{{a}^{2}}{{b}^{2}}=\frac{1}{{a}^{–2}{b}^{2}}$
2. $\frac{3{x}^{–1}}{{y}^{2}}=\frac{3}{x{y}^{2}}$
3. $\frac{4m{n}^{2}}{{x}^{3}}=\frac{4}{{m}^{–1}{n}^{–2}{x}^{3}}$
4. $\frac{{a}^{–1}{b}^{–3}}{3}=\frac{1}{3a{b}^{3}}$
5. $\frac{3{c}^{–\frac{2}{3}}}{7}=\frac{3}{7{c}^{\frac{2}{3}}}$
6. $\frac{2{x}^{\frac{1}{4}}}{5{y}^{2}}=\frac{2}{5{x}^{–\frac{1}{4}}{y}^{2}}$
7. $\frac{{m}^{–3}}{5}=\frac{1}{5{m}^{3}}$
8. $\frac{3{a}^{–2}{b}^{3}}{{c}^{4}}=\frac{3}{{a}^{2}{b}^{–3}{c}^{4}}$
9. ${x}^{–\frac{1}{2}}{y}^{2}=\frac{1}{{x}^{\frac{1}{2}}{y}^{–2}}$
10. ${a}^{–\frac{2}{3}}{b}^{3}{c}^{–2}=\frac{1}{{a}^{\frac{2}{3}}{b}^{–3}{c}^{2}}$
11. $\begin{array}{cc}\frac{3{x}^{–1}{y}^{–\frac{1}{2}}}{{y}^{3}}& =\frac{3}{x{y}^{\frac{1}{2}}{y}^{3}}\\ & =\frac{3}{x{y}^{\frac{1}{2}+3}}\\ & =\frac{3}{x{y}^{\frac{7}{2}}}\end{array}$
12. $\frac{2{m}^{–2}{n}^{\frac{1}{2}}}{9}=\frac{2}{9{m}^{2}{n}^{–\frac{1}{2}}}$
13. $\frac{2}{a}=2{a}^{–1}$
14. $\frac{3a}{{b}^{2}}=3a{b}^{–2}$
15. $\begin{array}{cc}\frac{{x}^{2}y}{{y}^{–2}}& ={x}^{2}y{y}^{2}\\ & ={x}^{2}{y}^{3}\end{array}$
16. $\frac{4}{{x}^{–\frac{1}{2}}{y}^{2}}=4{x}^{\frac{1}{2}}{y}^{–2}$
17. $\frac{3{a}^{5}}{7{x}^{–5}{y}^{–\frac{3}{4}}}=\frac{3{a}^{5}{x}^{5}{y}^{\frac{3}{4}}}{7}$
18. $\frac{1}{{a}^{–4}{b}^{–\frac{1}{3}}}={a}^{4}{b}^{\frac{1}{3}}$
19. $\begin{array}{cc}\frac{2{m}^{2}}{3{m}^{–3}{n}^{–\frac{1}{4}}}& =\frac{2{m}^{2}{m}^{3}{n}^{\frac{1}{4}}}{3}\\ & =\frac{2{m}^{5}{n}^{\frac{1}{4}}}{3}\end{array}$
20. $\frac{{a}^{3}}{{x}^{2}{y}^{–\frac{1}{2}}}={a}^{3}{x}^{–2}{y}^{\frac{1}{2}}$
21. $\begin{array}{cc}\frac{3{a}^{2}{b}^{3}}{{a}^{–1}x}& =3{a}^{2}{b}^{3}a{x}^{–1}\\ & =3{a}^{3}{b}^{3}{x}^{–1}\end{array}$
22. $\begin{array}{cc}\frac{3x{y}^{2}{z}^{3}}{{x}^{–1}{y}^{–2}{z}^{–3}}& =3x{y}^{2}{z}^{3}x{y}^{2}{z}^{3}\\ & =3{x}^{2}{y}^{4}{z}^{6}\end{array}$
23. $\begin{array}{cc}\frac{{m}^{–2}{n}^{–1}{x}^{–\frac{1}{2}}}{{m}^{–4}{n}^{–5}{x}^{–2}}& ={m}^{–2}{n}^{–1}{x}^{–\frac{1}{2}}{m}^{4}{n}^{5}{x}^{2}\\ & ={m}^{2}{n}^{4}{x}^{\frac{3}{2}}\end{array}$