Question

1. $\frac{22ab^{-1}}{2a^{-1}b^{-1}}$2. $\frac{9^{-1}}{9^{-2}}$3. $\frac{2x^{-1}y^{-2}}{14xy}$4. $\frac{9a}{3a^{-1}b^{-1}}$5. $\frac{4x^{-3}}{16x^{-4}}$6. $\frac{7y^{3}}{21y^{-2}}$7. $\frac{8x^{3}}{32x^{-3}}$8. $\frac{20c^{-2}d^{-3}}{2cd^{-3}}$9. $\frac{27x^{-3}y}{3x^{-2}y^{3}}$10. $\frac{9a^{-3}b}{54ab}$11. $\frac{36x^{-4}}{6xy^{-3}}$12. $\frac{24ab^{-1}}{4a^{-3}b}$13. $\frac{5}{5^{-2}}$14. $\frac{4a^{-3}b}{20a^{-2}b^{-1}}$15. $\frac{2ab}{18a^{-3}b^{-1}}$16. $\frac{14x^{-2}y}{2x^{-3}y^{-1}}$17. $\frac{3a^{-6}b}{9ab^{-7}}$18. $\frac{21a^{-4}b}{7b^{3}}$19. $\frac{5p^{-4}q^{-2}}{100p^{-4}}$20. $\frac{81m^{-3}}{9m^{-2}n}$21. $\frac{5r^{-2}t^{-1}}{25r^{-3}t}$22. $\frac{4a^{2}b}{24a^{-1}b^{-3}}$23. $\frac{7b^{-5}c}{49c^{2}}$24. $\frac{42x^{-4}y^{-6}}{6xy^{-3}}$

Explanation:

Step1: Simplify coefficients and constants

Use exponent rule $x^{-n}=\frac{1}{x^n}$, $\frac{x^m}{x^n}=x^{m-n}$
---

1. $\frac{22ab^{-1}}{2a^{-1}b^{-1}}$

Step1: Simplify coefficients, $a$ terms

$\frac{22}{2} \cdot a^{1-(-1)} \cdot b^{-1-(-1)} = 11a^2b^0$

Step2: Simplify $b^0=1$

$11a^2$

---

2. $\frac{9^{-1}}{9^{-2}}$

Step1: Apply exponent subtraction rule

$9^{-1-(-2)}=9^{1}$

Step2: Evaluate the power

$9$

---

3. $\frac{2x^{-1}y^{-2}}{14xy}$

Step1: Simplify coefficients, $x$/$y$ terms

$\frac{2}{14} \cdot x^{-1-1} \cdot y^{-2-1} = \frac{1}{7}x^{-2}y^{-3}$

Step2: Rewrite with positive exponents

$\frac{1}{7x^2y^3}$

---

4. $\frac{9a}{3a^{-1}b^{-2}}$

Step1: Simplify coefficients, $a$/$b$ terms

$\frac{9}{3} \cdot a^{1-(-1)} \cdot b^{0-(-2)} = 3a^2b^2$

---

5. $\frac{4x^{-3}}{16x^{-4}}$

Step1: Simplify coefficients, $x$ terms

$\frac{4}{16} \cdot x^{-3-(-4)} = \frac{1}{4}x^{1}$

Step2: Simplify expression

$\frac{x}{4}$

---

6. $\frac{7y^3}{21y^{-2}}$

Step1: Simplify coefficients, $y$ terms

$\frac{7}{21} \cdot y^{3-(-2)} = \frac{1}{3}y^{5}$

Step2: Rewrite expression

$\frac{y^5}{3}$

---

7. $\frac{8x^3}{32x^{-3}}$

Step1: Simplify coefficients, $x$ terms

$\frac{8}{32} \cdot x^{3-(-3)} = \frac{1}{4}x^{6}$

Step2: Rewrite expression

$\frac{x^6}{4}$

---

8. $\frac{20c^{-2}d^{-3}}{2cd^{-3}}$

Step1: Simplify coefficients, $c$/$d$ terms

$\frac{20}{2} \cdot c^{-2-1} \cdot d^{-3-(-3)} = 10c^{-3}d^0$

Step2: Simplify $d^0=1$, rewrite $c^{-3}$

$\frac{10}{c^3}$

---

9. $\frac{27x^{-3}y}{3x^{-2}y^4}$

Step1: Simplify coefficients, $x$/$y$ terms

$\frac{27}{3} \cdot x^{-3-(-2)} \cdot y^{1-4} = 9x^{-1}y^{-3}$

Step2: Rewrite with positive exponents

$\frac{9}{xy^3}$

---

10. $\frac{9a^{-2}b}{54ab}$

Step1: Simplify coefficients, $a$/$b$ terms

$\frac{9}{54} \cdot a^{-2-1} \cdot b^{1-1} = \frac{1}{6}a^{-3}b^0$

Step2: Simplify $b^0=1$, rewrite $a^{-3}$

$\frac{1}{6a^3}$

---

11. $\frac{36x^{-2}}{6xy^{-3}}$

Step1: Simplify coefficients, $x$/$y$ terms

$\frac{36}{6} \cdot x^{-2-1} \cdot y^{0-(-3)} = 6x^{-3}y^{3}$

Step2: Rewrite with positive exponents

$\frac{6y^3}{x^3}$

---

12. $\frac{24ab^{-1}}{4a^{-3}b}$

Step1: Simplify coefficients, $a$/$b$ terms

$\frac{24}{4} \cdot a^{1-(-3)} \cdot b^{-1-1} = 6a^4b^{-2}$

Step2: Rewrite with positive exponents

$\frac{6a^4}{b^2}$

---

13. $\frac{5}{5^{-2}}$

Step1: Apply exponent subtraction rule

$5^{1-(-2)}=5^3$

Step2: Evaluate the power

$125$

---

14. $\frac{4a^{-3}b}{20a^{-2}b^{-1}}$

Step1: Simplify coefficients, $a$/$b$ terms

$\frac{4}{20} \cdot a^{-3-(-2)} \cdot b^{1-(-1)} = \frac{1}{5}a^{-1}b^{2}$

Step2: Rewrite with positive exponents

$\frac{b^2}{5a}$

---

15. $\frac{2ab}{18a^{-3}b^{-1}}$

Step1: Simplify coefficients, $a$/$b$ terms

$\frac{2}{18} \cdot a^{1-(-3)} \cdot b^{1-(-1)} = \frac{1}{9}a^4b^2$

Step2: Rewrite expression

$\frac{a^4b^2}{9}$

---

16. $\frac{14x^{-2}y}{2x^{-3}y^{-1}}$

Step1: Simplify coefficients, $x$/$y$ terms

$\frac{14}{2} \cdot x^{-2-(-3)} \cdot y^{1-(-1)} = 7x^{1}y^{2}$

Step2: Rewrite expression

$7xy^2$

---

17. $\frac{3a^{-6}b}{9ab^{-2}}$

Step1: Simplify coefficients, $a$/$b$ terms

$\frac{3}{9} \cdot a^{-6-1} \cdot b^{1-(-2)} = \frac{1}{3}a^{-7}b^{3}$

Step2: Rewrite with positive exponents

$\frac{b^3}{3a^7}$

---

18. $\frac{21a^{-4}b}{7b^3}$

Step1: Simplify coefficients, $a$/$b$ terms

$\frac{21}{7} \cdot a^{-4-0} \cdot b^{1-3} = 3a^{-4}b^{-2}$

Step2: Rewrite with positive exponents

$\frac{3}{a^4b^2}$

---

19. $\frac{5p^{-4}q^{-2}}{100p^{-3}}$

Step1: Simplify coefficients, $p$/$q$ terms

$\frac{5}{100} \cdot p^{-4-(-3)} \cdot q^{-2-0} = \frac{1}{20}p^{-1}q^{-2}$

Step2: Rewrite with positive exponents

$\frac{1}{20pq^2}$

---

20. $\frac{81m^{-2}}{9m^{-4}n}$

Step1: Simplify coefficients, $m$/$n$ terms

$\frac{81}{9} \cdot m^{-2-(-4)} \cdot n^{0-1} = 9m^{2}n^{-1}$

Step2: Rewrite with positive exponents

$\frac{9m^2}{n}$

---

21. $\frac{5r^{-2}t^{-1}}{25r^{-3}t}$

Step1: Simplify coefficients, $r$/$t$ terms

$\frac{5}{25} \cdot r^{-2-(-3)} \cdot t^{-1-1} = \frac{1}{5}r^{1}t^{-2}$

Step2: Rewrite with positive exponents

$\frac{r}{5t^2}$

---

22. $\frac{4a^2b}{24a^{-1}b^{-3}}$

Step1: Simplify coefficients, $a$/$b$ terms

$\frac{4}{24} \cdot a^{2-(-1)} \cdot b^{1-(-3)} = \frac{1}{6}a^3b^4$

Step2: Rewrite expression

$\frac{a^3b^4}{6}$

---

23. $\frac{7b^{-2}c}{49c^2}$

Step1: Simplify coefficients, $b$/$c$ terms

$\frac{7}{49} \cdot b^{-2-0} \cdot c^{1-2} = \frac{1}{7}b^{-2}c^{-1}$

Step2: Rewrite with positive exponents

$\frac{1}{7b^2c}$

---

24. $\frac{42x^{-4}y^{-6}}{6xy^{-3}}$

Step1: Simplify coefficients, $x$/$y$ terms

$\frac{42}{6} \cdot x^{-4-1} \cdot y^{-6-(-3)} = 7x^{-5}y^{-3}$

Step2: Rewrite with positive exponents

$\frac{7}{x^5y^3}$

Answer:

1. $11a^2$
2. $9$
3. $\frac{1}{7x^2y^3}$
4. $3a^2b^2$
5. $\frac{x}{4}$
6. $\frac{y^5}{3}$
7. $\frac{x^6}{4}$
8. $\frac{10}{c^3}$
9. $\frac{9}{xy^3}$
10. $\frac{1}{6a^3}$
11. $\frac{6y^3}{x^3}$
12. $\frac{6a^4}{b^2}$
13. $125$
14. $\frac{b^2}{5a}$
15. $\frac{a^4b^2}{9}$
16. $7xy^2$
17. $\frac{b^3}{3a^7}$
18. $\frac{3}{a^4b^2}$
19. $\frac{1}{20pq^2}$
20. $\frac{9m^2}{n}$
21. $\frac{r}{5t^2}$
22. $\frac{a^3b^4}{6}$
23. $\frac{1}{7b^2c}$
24. $\frac{7}{x^5y^3}$