Question

1. \\(\frac{2^{10}}{2^4}\\) = \\(\frac{\quad}{1}\\)
2. \\(\frac{x^8}{x}\\) = \\(\frac{\quad}{1}\\)
3. \\(\frac{6a^6}{a^4}\\)
4. \\(\frac{40r^3}{8r^6}\\)
5. \\(\frac{3k^{10}}{15k^7}\\)
6. \\(\frac{50k^7}{10k^7}\\)
7. \\(\frac{42x^6y^4}{6x^3y^7}\\)
8. \\(\frac{9x^7y^3}{18x^2y^{10}}\\)
9. \\(\frac{6x^3y^{10}}{36xy^4}\\)
10. \\(\frac{p^9}{p^{15}} = \frac{1}{\quad}\\)
11. \\(\frac{10p^4}{5p^{10}}\\)
12. \\(\frac{4p^7}{2p^2}\\)
13. \\(\frac{6v^3}{9v^7}\\)
14. \\(\frac{12x^9y^7}{3x^7y^3}\\)
15. \\(\frac{50b^2}{10b}\\)
16. \\(\frac{12x^3y^5}{20x^9y^7}\\)
17. \\(\frac{8x^3y^8}{10x^5y^7}\\)

Explanation:

Step1: Apply exponent rule $\frac{x^m}{x^n}=x^{m-n}$

1) $\frac{z^n}{z^4}=z^{n-4}$

3) $\frac{x^8}{x^1}=x^{8-1}=x^7$

4) $\frac{p^2}{p^{10}}=p^{2-10}=p^{-8}=\frac{1}{p^8}$

Step2: Simplify coefficients + exponents

5) $\frac{6a^6}{a^4}=6a^{6-4}=6a^2$

6) $\frac{10p^4}{5p^{10}}=2p^{4-10}=2p^{-6}=\frac{2}{p^6}$

7) $\frac{40r^3}{8r^6}=5r^{3-6}=5r^{-3}=\frac{5}{r^3}$

8) $\frac{4p^7}{2p^2}=2p^{7-2}=2p^5$

9) $\frac{3k^{10}}{15k^7}=\frac{1}{5}k^{10-7}=\frac{k^3}{5}$

10) $\frac{6v^3}{9v^7}=\frac{2}{3}v^{3-7}=\frac{2}{3v^4}$

11) $\frac{50k^7}{10k^7}=5k^{7-7}=5$

12) $\frac{12x^9y^7}{3x^7y^3}=4x^{9-7}y^{7-3}=4x^2y^4$

13) $\frac{42x^6y^4}{6x^5y^2}=7x^{6-5}y^{4-2}=7xy^2$

14) $\frac{50a^2}{10b}=5\frac{a^2}{b}$

15) $\frac{9x^7y^2}{18x^2y^{10}}=\frac{1}{2}x^{7-2}y^{2-10}=\frac{x^5}{2y^8}$

16) $\frac{12x^3y^5}{20x^9y^7}=\frac{3}{5}x^{3-9}y^{5-7}=\frac{3}{5x^6y^2}$

17) $\frac{6x^3y^{10}}{36xy^4}=\frac{1}{6}x^{3-1}y^{10-4}=\frac{x^2y^6}{6}$

18) $\frac{8x^3y^8}{10x^5y^7}=\frac{4}{5}x^{3-5}y^{8-7}=\frac{4y}{5x^2}$

Answer:

1. $z^{n-4}$
2. $x^7$
3. $\frac{1}{p^8}$
4. $6a^2$
5. $\frac{2}{p^6}$
6. $\frac{5}{r^3}$
7. $2p^5$
8. $\frac{k^3}{5}$
9. $\frac{2}{3v^4}$
10. $5$
11. $4x^2y^4$
12. $7xy^2$
13. $\frac{5a^2}{b}$
14. $\frac{x^5}{2y^8}$
15. $\frac{3}{5x^6y^2}$
16. $\frac{x^2y^6}{6}$
17. $\frac{4y}{5x^2}$