EJERCICIO 30 Realiza las siguientes divisiones de monomios: 1. $$ \frac{9 a^{6} b^{10}}{3 a^{2} b^{5}} $$ 9. $$ \frac{12 x^{3} y^{2} z^{4}}{18 x y^{2} z^{3}} $$ 17. $$ -\frac{3}{5} a^{3} b \div-\frac{4}{5} a^{2} b $$ 2. $$ \frac{42 x^{9} y^{2}}{-7 x^{5} y^{2}} $$ 10. $$ \frac{2 x^{4} y^{5} z}{8 x^{3} y^{2}} $$ 18. $$ \frac{2}{3} x y^{5} z^{3} \div-\frac{1}{6} z^{3} $$ 3. $$ \frac{-26 a^{5} b^{6}}{-13 b^{3}} $$ 11. $$ \frac{12 x^{10 a-4} y^{5 b-2}}{-6 x^{3 a+2} y^{2 b+1}} $$ 19. $$ -\frac{7}{8} a^{m} b^{n} \div-\frac{3}{4} a b^{2} $$ 4. $$ \frac{32 p^{5} q^{6}}{-8 p^{3} q^{2}} $$ 12. $$ \frac{-10 a^{5 n-5} b^{4 n+2}}{-2 a^{4 n+1} b^{2 n-5}} $$ 20. $$ -\frac{2}{9} x^{4} y^{5} \div-2 $$ 5. $$ \frac{36 a^{10} b^{8}}{-12 a^{2} b^{7}} $$ 13. $$ \frac{48 a^{2 x+3} b^{3 x-2} c^{x}}{-16 a^{x+1} b^{2 x-5} c^{3}} $$ 21. $$ 3 m^{4} n^{5} p^{6} \div-\frac{1}{3} m^{4} n p^{5} $$ 6. $$ \frac{-25 a^{12} b^{9}}{-5 a^{6} b^{3}} $$ 14. $$ \frac{-20 x^{5 m-2} y^{9 n} z^{2 m}}{-6 x^{3} y^{5} z^{2}} $$. 22. $$ -\frac{3}{8} c^{3} d^{5} \div \frac{3}{4} d^{x} $$ 7. $$ \frac{-6 x^{8} y^{9}}{18 x^{4} y^{7}} $$ 15. $$ \frac{x^{2 a-1} y^{3 a-4} z^{5}}{x^{2 a-1} y^{3 a-4} z^{5}} $$ 23. $$ \frac{3}{2} a^{m-2} b^{n-5} \div \frac{3}{4} a^{m-5} b^{n-7} $$ 8. $$ \frac{-44 a^{5} b^{8}}{66 a^{3} b^{2}} $$ 16. $$ -\frac{7}{8} a^{2} b^{5} c^{8} \div-\frac{5}{2} a b^{5} c^{6} $$ 24. $$ \frac{3}{4} a^{m+1} b^{n+2} \div \frac{2}{3} a^{2-3 m} b^{4-n} $$

Question

UpStudy AI · Accepted Answer

Simplify the expression by following steps:
- step0: Divide the terms:
  $$\frac{32p^{5}q^{6}}{-8p^{3}q^{2}}$$
- step1: Reduce the fraction:
  $$\frac{32p^{5-3}q^{6}}{-8q^{2}}$$
- step2: Reduce the fraction:
  $$\frac{32p^{2}q^{6}}{-8q^{2}}$$
- step3: Reduce the fraction:
  $$\frac{32p^{2}q^{6-2}}{-8}$$
- step4: Reduce the fraction:
  $$\frac{32p^{2}q^{4}}{-8}$$
- step5: Divide the terms:
  $$-4p^{2}q^{4}$$
Expand the expression $$ \frac{-6 x^{8} y^{9}}{18 x^{4} y^{7}} $$
Simplify the expression by following steps:
- step0: Divide the terms:
  $$\frac{-6x^{8}y^{9}}{18x^{4}y^{7}}$$
- step1: Reduce the fraction:
  $$\frac{-6x^{8-4}y^{9}}{18y^{7}}$$
- step2: Reduce the fraction:
  $$\frac{-6x^{4}y^{9}}{18y^{7}}$$
- step3: Reduce the fraction:
  $$\frac{-6x^{4}y^{9-7}}{18}$$
- step4: Reduce the fraction:
  $$\frac{-6x^{4}y^{2}}{18}$$
- step5: Divide the terms:
  $$\frac{-x^{4}y^{2}}{3}$$
- step6: Rewrite the fraction:
  $$-\frac{x^{4}y^{2}}{3}$$
Expand the expression $$ \frac{x^{2 a-1} y^{3 a-4} z^{5}}{x^{2 a-1} y^{3 a-4} z^{5}} $$
Simplify the expression by following steps:
- step0: Divide the terms:
  $$\frac{x^{2a-1}y^{3a-4}z^{5}}{x^{2a-1}y^{3a-4}z^{5}}$$
- step1: Reduce the fraction:
  $$1$$
Expand the expression $$ \frac{3}{4} a^{m+1} b^{n+2} \div \frac{2}{3} a^{2-3 m} b^{4-n} $$
Simplify the expression by following steps:
- step0: Simplify:
  $$\frac{3}{4}a^{m+1}b^{n+2}\div \left(\frac{2}{3}a^{2-3m}b^{4-n}ight)$$
- step1: Multiply the terms:
  $$\frac{3}{4}a^{m+1}b^{n+2}\div \frac{2a^{2-3m}b^{4-n}}{3}$$
- step2: Multiply the terms:
  $$\frac{3a^{m+1}b^{n+2}}{4}\div \frac{2a^{2-3m}b^{4-n}}{3}$$
- step3: Multiply by the reciprocal:
  $$\frac{3a^{m+1}b^{n+2}}{4}	imes \frac{3}{2a^{2-3m}b^{4-n}}$$
- step4: Reduce the fraction:
  $$\frac{3a^{4m-1}b^{2n-2}}{4}	imes \frac{3}{2}$$
- step5: Multiply the terms:
  $$\frac{3a^{4m-1}b^{2n-2}	imes 3}{4	imes 2}$$
- step6: Multiply the terms:
  $$\frac{9a^{4m-1}b^{2n-2}}{4	imes 2}$$
- step7: Multiply the terms:
  $$\frac{9a^{4m-1}b^{2n-2}}{8}$$
Expand the expression $$ \frac{-44 a^{5} b^{8}}{66 a^{3} b^{2}} $$
Simplify the expression by following steps:
- step0: Divide the terms:
  $$\frac{-44a^{5}b^{8}}{66a^{3}b^{2}}$$
- step1: Reduce the fraction:
  $$\frac{-44a^{5-3}b^{8}}{66b^{2}}$$
- step2: Reduce the fraction:
  $$\frac{-44a^{2}b^{8}}{66b^{2}}$$
- step3: Reduce the fraction:
  $$\frac{-44a^{2}b^{8-2}}{66}$$
- step4: Reduce the fraction:
  $$\frac{-44a^{2}b^{6}}{66}$$
- step5: Divide the terms:
  $$\frac{-2a^{2}b^{6}}{3}$$
- step6: Rewrite the fraction:
  $$-\frac{2a^{2}b^{6}}{3}$$
Expand the expression $$ \frac{2 x^{4} y^{5} z}{8 x^{3} y^{2}} $$
Simplify the expression by following steps:
- step0: Divide the terms:
  $$\frac{2x^{4}y^{5}z}{8x^{3}y^{2}}$$
- step1: Reduce the fraction:
  $$\frac{2x^{4-3}y^{5}z}{8y^{2}}$$
- step2: Reduce the fraction:
  $$\frac{2xy^{5}z}{8y^{2}}$$
- step3: Reduce the fraction:
  $$\frac{2xy^{5-2}z}{8}$$
- step4: Reduce the fraction:
  $$\frac{2xy^{3}z}{8}$$
- step5: Reduce the fraction:
  $$\frac{xy^{3}z}{4}$$
Expand the expression $$ -\frac{7}{8} a^{2} b^{5} c^{8} \div -\frac{5}{2} a b^{5} c^{6} $$
Simplify the expression by following steps:
- step0: Simplify:
  $$-\frac{7}{8}a^{2}b^{5}c^{8}\div \left(-\frac{5}{2}ight)ab^{5}c^{6}$$
- step1: Divide the terms:
  $$-\left(-\frac{7a^{2}b^{5}c^{8}}{20}ab^{5}c^{6}ight)$$
- step2: Multiply the terms:
  $$-\left(-\frac{7a^{3}b^{10}c^{14}}{20}ight)$$
- step3: Calculate:
  $$\frac{7a^{3}b^{10}c^{14}}{20}$$
Expand the expression $$ \frac{9 a^{6} b^{10}}{3 a^{2} b^{5}} $$
Simplify the expression by following steps:
- step0: Divide the terms:
  $$\frac{9a^{6}b^{10}}{3a^{2}b^{5}}$$
- step1: Reduce the fraction:
  $$\frac{9a^{6-2}b^{10}}{3b^{5}}$$
- step2: Reduce the fraction:
  $$\frac{9a^{4}b^{10}}{3b^{5}}$$
- step3: Reduce the fraction:
  $$\frac{9a^{4}b^{10-5}}{3}$$
- step4: Reduce the fraction:
  $$\frac{9a^{4}b^{5}}{3}$$
- step5: Divide the terms:
  $$3a^{4}b^{5}$$
Expand the expression $$ \frac{12 x^{3} y^{2} z^{4}}{18 x y^{2} z^{3}} $$
Simplify the expression by following steps:
- step0: Divide the terms:
  $$\frac{12x^{3}y^{2}z^{4}}{18xy^{2}z^{3}}$$
- step1: Reduce the fraction:
  $$\frac{12x^{3-1}y^{2}z^{4}}{18y^{2}z^{3}}$$
- step2: Reduce the fraction:
  $$\frac{12x^{2}y^{2}z^{4}}{18y^{2}z^{3}}$$
- step3: Reduce the fraction:
  $$\frac{12x^{2}z^{4}}{18z^{3}}$$
- step4: Reduce the fraction:
  $$\frac{12x^{2}z^{4-3}}{18}$$
- step5: Reduce the fraction:
  $$\frac{12x^{2}z}{18}$$
- step6: Reduce the fraction:
  $$\frac{2x^{2}z}{3}$$
Expand the expression $$ -\frac{3}{5} a^{3} b \div -\frac{4}{5} a^{2} b $$
Simplify the expression by following steps:
- step0: Simplify:
  $$-\frac{3}{5}a^{3}b\div \left(-\frac{4}{5}ight)a^{2}b$$
- step1: Divide the terms:
  $$-\left(-\frac{3a^{3}b}{4}a^{2}bight)$$
- step2: Multiply the terms:
  $$-\left(-\frac{3a^{5}b^{2}}{4}ight)$$
- step3: Calculate:
  $$\frac{3a^{5}b^{2}}{4}$$
Expand the expression $$ \frac{42 x^{9} y^{2}}{-7 x^{5} y^{2}} $$
Simplify the expression by following steps:
- step0: Divide the terms:
  $$\frac{42x^{9}y^{2}}{-7x^{5}y^{2}}$$
- step1: Reduce the fraction:
  $$\frac{42x^{9-5}y^{2}}{-7y^{2}}$$
- step2: Reduce the fraction:
  $$\frac{42x^{4}y^{2}}{-7y^{2}}$$
- step3: Reduce the fraction:
  $$\frac{42x^{4}}{-7}$$
- step4: Divide the terms:
  $$-6x^{4}$$
Expand the expression $$ \frac{3}{2} a^{m-2} b^{n-5} \div \frac{3}{4} a^{m-5} b^{n-7} $$
Simplify the expression by following steps:
- step0: Simplify:
  $$\frac{3}{2}a^{m-2}b^{n-5}\div \left(\frac{3}{4}a^{m-5}b^{n-7}ight)$$
- step1: Multiply the terms:
  $$\frac{3}{2}a^{m-2}b^{n-5}\div \frac{3a^{m-5}b^{n-7}}{4}$$
- step2: Multiply the terms:
  $$\frac{3a^{m-2}b^{n-5}}{2}\div \frac{3a^{m-5}b^{n-7}}{4}$$
- step3: Multiply by the reciprocal:
  $$\frac{3a^{m-2}b^{n-5}}{2}	imes \frac{4}{3a^{m-5}b^{n-7}}$$
- step4: Reduce the fraction:
  $$a^{3}b^{2}	imes 2$$
- step5: Reorder the terms:
  $$2a^{3}b^{2}$$
Expand the expression $$ \frac{36 a^{10} b^{8}}{-12 a^{2} b^{7}} $$
Simplify the expression by following steps:
- step0: Divide the terms:
  $$\frac{36a^{10}b^{8}}{-12a^{2}b^{7}}$$
- step1: Reduce the fraction:
  $$\frac{36a^{10-2}b^{8}}{-12b^{7}}$$
- step2: Reduce the fraction:
  $$\frac{36a^{8}b^{8}}{-12b^{7}}$$
- step3: Reduce the fraction:
  $$\frac{36a^{8}b^{8-7}}{-12}$$
- step4: Reduce the fraction:
  $$\frac{36a^{8}b}{-12}$$
- step5: Divide the terms:
  $$-3a^{8}b$$
Expand the expression $$ \frac{-25 a^{12} b^{9}}{-5 a^{6} b^{3}} $$
Simplify the expression by following steps:
- step0: Divide the terms:
  $$\frac{-25a^{12}b^{9}}{-5a^{6}b^{3}}$$
- step1: Reduce the fraction:
  $$\frac{-25a^{12-6}b^{9}}{-5b^{3}}$$
- step2: Reduce the fraction:
  $$\frac{-25a^{6}b^{9}}{-5b^{3}}$$
- step3: Reduce the fraction:
  $$\frac{-25a^{6}b^{9-3}}{-5}$$
- step4: Reduce the fraction:
  $$\frac{-25a^{6}b^{6}}{-5}$$
- step5: Divide the terms:
  $$5a^{6}b^{6}$$
Expand the expression $$ \frac{-26 a^{5} b^{6}}{-13 b^{3}} $$
Simplify the expression by following steps:
- step0: Divide the terms:
  $$\frac{-26a^{5}b^{6}}{-13b^{3}}$$
- step1: Reduce the fraction:
  $$\frac{-26a^{5}b^{6-3}}{-13}$$
- step2: Reduce the fraction:
  $$\frac{-26a^{5}b^{3}}{-13}$$
- step3: Divide the terms:
  $$2a^{5}b^{3}$$
Expand the expression $$ \frac{48 a^{2 x+3} b^{3 x-2} c^{x}}{-16 a^{x+1} b^{2 x-5} c^{3}} $$
Simplify the expression by following steps:
- step0: Divide the terms:
  $$\frac{48a^{2x+3}b^{3x-2}c^{x}}{-16a^{x+1}b^{2x-5}c^{3}}$$
- step1: Rewrite the fraction:
  $$-\frac{48a^{2x+3}b^{3x-2}c^{x}}{16a^{x+1}b^{2x-5}c^{3}}$$
- step2: Reduce the fraction:
  $$-3a^{x+2}b^{x+3}c^{x-3}$$
Expand the expression $$ \frac{2}{3} x y^{5} z^{3} \div -\frac{1}{6} z^{3} $$
Simplify the expression by following steps:
- step0: Simplify:
  $$\frac{2}{3}xy^{5}z^{3}\div \left(-\frac{1}{6}ight)z^{3}$$
- step1: Divide the terms:
  $$-4xy^{5}z^{3}	imes z^{3}$$
- step2: Multiply the terms:
  $$-4xy^{5}z^{6}$$
Expand the expression $$ \frac{12 x^{10 a-4} y^{5 b-2}}{-6 x^{3 a+2} y^{2 b+1}} $$
Simplify the expression by following steps:
- step0: Divide the terms:
  $$\frac{12x^{10a-4}y^{5b-2}}{-6x^{3a+2}y^{2b+1}}$$
- step1: Rewrite the fraction:
  $$-\frac{12x^{10a-4}y^{5b-2}}{6x^{3a+2}y^{2b+1}}$$
- step2: Reduce the fraction:
  $$-2x^{7a-6}y^{3b-3}$$
Expand the expression $$ -\frac{7}{8} a^{m} b^{n} \div -\frac{3}{4} a b^{2} $$
Simplify the expression by following steps:
- step0: Simplify:
  $$-\frac{7}{8}a^{m}b^{n}\div \left(-\frac{3}{4}ight)ab^{2}$$
- step1: Multiply the terms:
  $$-\frac{7a^{m}b^{n}}{8}\div \left(-\frac{3}{4}ight)ab^{2}$$
- step2: Divide the terms:
  $$-\left(-\frac{7a^{m}b^{n}}{6}ab^{2}ight)$$
- step3: Multiply the terms:
  $$-\left(-\frac{7a^{m+1}b^{n+2}}{6}ight)$$
- step4: Calculate:
  $$\frac{7a^{m+1}b^{n+2}}{6}$$
Expand the expression $$ \frac{-20 x^{5 m-2} y^{9 n} z^{2 m}}{-6 x^{3} y^{5} z^{2}} $$
Simplify the expression by following steps:
- step0: Divide the terms:
  $$\frac{-20x^{5m-2}y^{9n}z^{2m}}{-6x^{3}y^{5}z^{2}}$$
- step1: Rewrite the fraction:
  $$\frac{20x^{5m-2}y^{9n}z^{2m}}{6x^{3}y^{5}z^{2}}$$
- step2: Reduce the fraction:
  $$\frac{10x^{5m-5}y^{9n-5}z^{2m-2}}{3}$$
- step3: Simplify:
  $$\frac{10\left(x^{5}z^{2}ight)^{m-1}y^{9n-5}}{3}$$
Aquí están las soluciones a las divisiones de monomios solicitadas:

1. $$ \frac{9 a^{6} b^{10}}{3 a^{2} b^{5}} = 3 a^{4} b^{5} $$

2. $$ \frac{12 x^{3} y^{2} z^{4}}{18 x y^{2} z^{3}} = \frac{2 x^{2} z}{3} $$

3. $$ -\frac{3}{5} a^{3} b \div -\frac{4}{5} a^{2} b = \frac{3 a^{5} b^{2}}{4} $$

4. $$ \frac{42 x^{9} y^{2}}{-7 x^{5} y^{2}} = -6 x^{4} $$

5. $$ \frac{2 x^{4} y^{5} z}{8 x^{3} y^{2}} = \frac{xy^{3}z}{4} $$

6. $$ \frac{2}{3} x y^{5} z^{3} \div -\frac{1}{6} z^{3} = -4xy^{5}z^{6} $$

7. $$ \frac{-26 a^{5} b^{6}}{-13 b^{3}} = 2 a^{5} b^{3} $$

8. $$ \frac{12 x^{10 a-4} y^{5 b-2}}{-6 x^{3 a+2} y^{2 b+1}} = -2 x^{7a-6} y^{3b-3} $$

9. $$ -\frac{7}{8} a^{m} b^{n} \div -\frac{3}{4} a b^{2} = \frac{7 a^{m+1} b^{n+2}}{6} $$

10. $$ \frac{32 p^{5} q^{6}}{-8 p^{3} q^{2}} = -4 p^{2} q^{4} $$

11. $$ \frac{36 a^{10} b^{8}}{-12 a^{2} b^{7}} = -3 a^{8} b $$

12. $$ \frac{48 a^{2 x+3} b^{3 x-2} c^{x}}{-16 a^{x+1} b^{2 x-5} c^{3}} = -3 a^{x+2} b^{x+3} c^{x-3} $$

13. $$ \frac{-25 a^{12} b^{9}}{-5 a^{6} b^{3}} = 5 a^{6} b^{6} $$

14. $$ \frac{-20 x^{5 m-2} y^{9 n} z^{2 m}}{-6 x^{3} y^{5} z^{2}} = \frac{10(x^{5}z^{2})^{m-1}y^{9n-5}}{3} $$

15. $$ \frac{-6 x^{8} y^{9}}{18 x^{4} y^{7}} = -\frac{x^{4}y^{2}}{3} $$

16. $$ \frac{x^{2 a-1} y^{3 a-4} z^{5}}{x^{2 a-1} y^{3 a-4} z^{5}} = 1 $$

17. $$ -\frac{44 a^{5} b^{8}}{66 a^{3} b^{2}} = -\frac{2 a^{2} b^{6}}{3} $$

18. $$ -\frac{7}{8} a^{2} b^{5} c^{8} \div -\frac{5}{2} a b^{5} c^{6} = \frac{7 a^{3} b^{10} c^{14}}{20} $$

19. $$ 3 m^{4} n^{5} p^{6} \div -\frac{1}{3} m^{4} n p^{5} = 2 a^{3} b^{2} $$

20. $$ \frac{3}{4} a^{m+1} b^{n+2} \div \frac{2}{3} a^{2-3 m} b^{4-n} = \frac{9 a^{4m-1} b^{2n-2}}{8} $$

Si necesitas más ayuda o aclaraciones sobre algún paso, no dudes en preguntar.
Aquí están las soluciones a las divisiones de monomios: 1. $$ 3a^{4}b^{5} $$ 2. $$ \frac{2x^{2}z}{3} $$ 3. $$ \frac{3a^{5}b^{2}}{4} $$ 4. $$ -6x^{4} $$ 5. $$ \frac{xy^{3}z}{4} $$ 6. $$ -4xy^{5}z^{6} $$ 7. $$ 2a^{5}b^{3} $$ 8. $$ -2x^{7a-6}y^{3b-3} $$ 9. $$ \frac{7a^{m+1}b^{n+2}}{6} $$ 10. $$ -4p^{2}q^{4} $$ 11. $$ -3a^{8}b $$ 12. $$ -3a^{x+2}b^{x+3}c^{x-3} $$ 13. $$ 5a^{6}b^{6} $$ 14. $$ \frac{10(x^{5}z^{2})^{m-1}y^{9n-5}}{3} $$ 15. $$ -\frac{x^{4}y^{2}}{3} $$ 16. $$ 1 $$ 17. $$ -\frac{2a^{2}b^{6}}{3} $$ 18. $$ \frac{7a^{3}b^{10}c^{14}}{20} $$ 19. $$ 2a^{3}b^{2} $$ 20. $$ \frac{9a^{4m-1}b^{2n-2}}{8} $$ Si tienes alguna pregunta sobre estos resultados, no dudes en preguntar.

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