Question

simplifying negative exponent challenge practice

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

Explanation:

Rule Reference:

Recall the negative exponent rule: $a^{-n} = \frac{1}{a^n}$ and $\frac{1}{a^{-n}} = a^n$, where $a
eq0$. Simplify coefficients first where possible.

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1. Step1: Rewrite negative exponent

$\frac{18}{2b^{-1}} = \frac{18b}{2}$

Step2: Simplify the fraction

$\frac{18b}{2} = 9b$

2. Step1: Apply negative exponent rule

$9^{-1} = \frac{1}{9}$

3. Step1: Rewrite negative exponent

$\frac{2x^{-1}}{14} = \frac{2}{14x}$

Step2: Simplify the fraction

$\frac{2}{14x} = \frac{1}{7x}$

4. Step1: Rewrite negative exponent

$\frac{9}{3b^{-1}} = \frac{9b}{3}$

Step2: Simplify the fraction

$\frac{9b}{3} = 3b$

5. Step1: Rewrite negative exponent

$\frac{4x^{-2}}{16} = \frac{4}{16x^2}$

Step2: Simplify the fraction

$\frac{4}{16x^2} = \frac{1}{4x^2}$

6. Step1: Rewrite negative exponent

$\frac{7}{21y^{-4}} = \frac{7y^4}{21}$

Step2: Simplify the fraction

$\frac{7y^4}{21} = \frac{y^4}{3}$

7. Step1: Rewrite negative exponent

$\frac{8}{32x^{-3}} = \frac{8x^3}{32}$

Step2: Simplify the fraction

$\frac{8x^3}{32} = \frac{x^3}{4}$

8. Step1: Rewrite negative exponent

$\frac{20}{2d^{-3}} = \frac{20d^3}{2}$

Step2: Simplify the fraction

$\frac{20d^3}{2} = 10d^3$

9. Step1: Rewrite negative exponent

$\frac{27}{3x^{-2}} = \frac{27x^2}{3}$

Step2: Simplify the fraction

$\frac{27x^2}{3} = 9x^2$

10. Step1: Rewrite negative exponent

$\frac{9a^{-3}}{54} = \frac{9}{54a^3}$

Step2: Simplify the fraction

$\frac{9}{54a^3} = \frac{1}{6a^3}$

11. Step1: Rewrite negative exponent

$\frac{36x^{-4}}{6} = \frac{36}{6x^4}$

Step2: Simplify the fraction

$\frac{36}{6x^4} = \frac{6}{x^4}$

12. Step1: Rewrite negative exponent

$\frac{24}{4a^{-3}} = \frac{24a^3}{4}$

Step2: Simplify the fraction

$\frac{24a^3}{4} = 6a^3$

13. Step1: Apply negative exponent rule

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

Step2: Calculate the power

$9^2 = 81$

14. Step1: Rewrite negative exponent

$\frac{4a^{-5}}{20} = \frac{4}{20a^5}$

Step2: Simplify the fraction

$\frac{4}{20a^5} = \frac{1}{5a^5}$

15. Step1: Rewrite negative exponent

$\frac{2}{18b^{-1}} = \frac{2b}{18}$

Step2: Simplify the fraction

$\frac{2b}{18} = \frac{b}{9}$

16. Step1: Rewrite negative exponent

$\frac{14}{2x^{-3}} = \frac{14x^3}{2}$

Step2: Simplify the fraction

$\frac{14x^3}{2} = 7x^3$

17. Step1: Rewrite negative exponent

$\frac{3}{9b^{-1}} = \frac{3b}{9}$

Step2: Simplify the fraction

$\frac{3b}{9} = \frac{b}{3}$

18. Step1: Rewrite negative exponent

$\frac{21a^{-4}}{7} = \frac{21}{7a^4}$

Step2: Simplify the fraction

$\frac{21}{7a^4} = \frac{3}{a^4}$

19. Step1: Rewrite negative exponent

$\frac{5q^{-4}}{100} = \frac{5}{100q^4}$

Step2: Simplify the fraction

$\frac{5}{100q^4} = \frac{1}{20q^4}$

20. Step1: Rewrite negative exponent

$\frac{81m^{-5}}{9} = \frac{81}{9m^5}$

Step2: Simplify the fraction

$\frac{81}{9m^5} = \frac{9}{m^5}$

21. Step1: Rewrite negative exponent

$\frac{5r^{-2}}{25} = \frac{5}{25r^2}$

Step2: Simplify the fraction

$\frac{5}{25r^2} = \frac{1}{5r^2}$

22. Step1: Rewrite negative exponent

$\frac{4}{24a^{-2}} = \frac{4a^2}{24}$

Step2: Simplify the fraction

$\frac{4a^2}{24} = \frac{a^2}{6}$

23. Step1: Rewrite negative exponent

$\frac{7b^{-4}}{49} = \frac{7}{49b^4}$

Step2: Simplify the fraction

$\frac{7}{49b^4} = \frac{1}{7b^4}$

24. Step1: Rewrite negative exponent

$\frac{42x^{-4}}{6} = \frac{42}{6x^4}$

Step2: Simplify the fraction

$\frac{42}{6x^4} = \frac{7}{x^4}$

Answer:

1. $9b$
2. $\frac{1}{9}$
3. $\frac{1}{7x}$
4. $3b$
5. $\frac{1}{4x^2}$
6. $\frac{y^4}{3}$
7. $\frac{x^3}{4}$
8. $10d^3$
9. $9x^2$
10. $\frac{1}{6a^3}$
11. $\frac{6}{x^4}$
12. $6a^3$
13. $81$
14. $\frac{1}{5a^5}$
15. $\frac{b}{9}$
16. $7x^3$
17. $\frac{b}{3}$
18. $\frac{3}{a^4}$
19. $\frac{1}{20q^4}$
20. $\frac{9}{m^5}$
21. $\frac{1}{5r^2}$
22. $\frac{a^2}{6}$
23. $\frac{1}{7b^4}$
24. $\frac{7}{x^4}$