6.5E: Mazoezi

Mazoezi hufanya kamili

Kurahisisha Maneno Kutumia Mali ya Quotient kwa Watazamaji

Katika mazoezi yafuatayo, kurahisisha.

Zoezi$\PageIndex{1}$

1. $\dfrac{x^{18}}{x^{3}}$
2. $\dfrac{5^{12}}{5^{3}}$

Zoezi$\PageIndex{2}$

1. $\dfrac{y^{20}}{y^{10}}$
2. $\dfrac{7^{16}}{7^{2}}$

Jibu

1. $y^{10}$
2. $7^{14}$

Zoezi$\PageIndex{3}$

1. $\dfrac{p^{21}}{p^{7}}$
2. $\dfrac{4^{16}}{4^{4}}$

Zoezi$\PageIndex{4}$

1. $\dfrac{u^{24}}{u^{3}}$
2. $\dfrac{9^{15}}{9^{5}}$

Jibu

1. $u^{21}$
2. $9^{10}$

Zoezi$\PageIndex{5}$

1. $\dfrac{q^{18}}{q^{36}}$
2. $\dfrac{10^{2}}{10^{3}}$

Zoezi$\PageIndex{6}$

1. $\dfrac{t^{10}}{t^{40}}$
2. $\dfrac{8^{3}}{8^{5}}$

Jibu

1. $\dfrac{1}{t^{30}}$
2. $\dfrac{1}{64}$

Zoezi$\PageIndex{7}$

1. $\dfrac{b}{b^{9}}$
2. $\dfrac{4}{4^{6}}$

Zoezi$\PageIndex{8}$

1. $\dfrac{x}{x^{7}}$
2. $\dfrac{10}{10^{3}}$

Jibu

1. $\dfrac{1}{x^{6}}$
2. $\dfrac{1}{100}$

Kurahisisha Maneno na Zero Exponents

Katika mazoezi yafuatayo, kurahisisha.

Zoezi$\PageIndex{9}$

1. $20^{0}$
2. $b^{0}$

Zoezi$\PageIndex{10}$

1. $13^0$
2. $k^{0}$

Jibu

1. 1
2. 1

Zoezi$\PageIndex{11}$

1. $-27^{0}$
2. $-\left(27^{0}\right)$

Zoezi$\PageIndex{12}$

1. $-15^{0}$
2. $-\left(15^{0}\right)$

Jibu

1. -1
2. -1

Zoezi$\PageIndex{13}$

1. $(25 x)^{0}$
2. $25 x^{0}$

Zoezi$\PageIndex{14}$

1. $(6 y)^{0}$
2. $6 y^{0}$

Jibu

1. 1
2. 6

Zoezi$\PageIndex{15}$

1. $(12 x)^{0}$
2. $\left(-56 p^{4} q^{3}\right)^{0}$

Zoezi$\PageIndex{16}$

1. 7$y^{0}(17 y)^{0}$
2. $\left(-93 c^{7} d^{15}\right)^{0}$

Jibu

1. 7
2. 1

Zoezi$\PageIndex{17}$

1. $12 n^{0}-18 m^{0}$
2. $(12 n)^{0}-(18 m)^{0}$

Zoezi$\PageIndex{18}$

1. $15 r^{0}-22 s^{0}$
2. $(15 r)^{0}-(22 s)^{0}$

Jibu

1. -7
2. 0

Kurahisisha Maneno Kutumia Quotient kwa Mali ya Nguvu

Katika mazoezi yafuatayo, kurahisisha.

Zoezi$\PageIndex{19}$

1. $\left(\dfrac{3}{4}\right)^{3}$
2. $\left(\dfrac{p}{2}\right)^{5}$
3. $\left(\dfrac{x}{y}\right)^{6}$

Zoezi$\PageIndex{20}$

1. $\left(\dfrac{2}{5}\right)^{2}$
2. $\left(\dfrac{x}{3}\right)^{4}$
3. $\left(\dfrac{a}{b}\right)^{5}$

Jibu

1. $\dfrac{4}{25}$
2. $\dfrac{x^{4}}{81}$
3. $\left(\dfrac{a}{b}\right)^{5}$

Zoezi$\PageIndex{21}$

1. $\left(\dfrac{a}{3 b}\right)^{4}$
2. $\left(\dfrac{5}{4 m}\right)^{2}$

Zoezi$\PageIndex{22}$

1. $\left(\dfrac{a}{3 b}\right)^{4}$
2. $\left(\dfrac{10}{3 q}\right)^{4}$

Jibu

1. $\dfrac{x^{3}}{8 y^{3}}$
2. $\dfrac{10,000}{81 q^{4}}$

Kurahisisha Maneno kwa kutumia Mali kadhaa

Katika mazoezi yafuatayo, kurahisisha.

Zoezi$\PageIndex{23}$

$\dfrac{\left(a^{2}\right)^{3}}{a^{4}}$

Zoezi$\PageIndex{24}$

$\dfrac{\left(p^{3}\right)^{4}}{p^{5}}$

Jibu

$p^{7}$

Zoezi$\PageIndex{25}$

$\dfrac{\left(y^{3}\right)^{4}}{y^{10}}$

Zoezi$\PageIndex{26}$

$\dfrac{\left(x^{4}\right)^{5}}{x^{15}}$

Jibu

$x^{5}$

Zoezi$\PageIndex{27}$

$\dfrac{u^{6}}{\left(u^{3}\right)^{2}}$

Zoezi$\PageIndex{28}$

$\dfrac{v^{20}}{\left(v^{4}\right)^{5}}$

Jibu

1

Zoezi$\PageIndex{29}$

$\dfrac{m^{12}}{\left(m^{8}\right)^{3}}$

Zoezi$\PageIndex{30}$

$\dfrac{n^{8}}{\left(n^{6}\right)^{4}}$

Jibu

$\dfrac{1}{n^{16}}$

Zoezi$\PageIndex{31}$

$\left(\dfrac{p^{9}}{p^{3}}\right)^{5}$

Zoezi$\PageIndex{32}$

$\left(\dfrac{q^{8}}{q^{2}}\right)^{3}$

Jibu

$q^{18}$

Zoezi$\PageIndex{33}$

$\left(\dfrac{r^{2}}{r^{6}}\right)^{3}$

Zoezi$\PageIndex{34}$

$\left(\dfrac{m^{4}}{m^{7}}\right)^{4}$

Jibu

$\dfrac{1}{m^{12}}$

Zoezi$\PageIndex{35}$

$\left(\dfrac{p}{r^{11}}\right)^{2}$

Zoezi$\PageIndex{36}$

$\left(\dfrac{a}{b^{6}}\right)^{3}$

Jibu

$\dfrac{a^{3}}{b^{18}}$

Zoezi$\PageIndex{37}$

$\left(\dfrac{w^{5}}{x^{3}}\right)^{8}$

Zoezi$\PageIndex{38}$

$\left(\dfrac{y^{4}}{z^{10}}\right)^{5}$

Jibu

$\dfrac{y^{20}}{z^{50}}$

Zoezi$\PageIndex{39}$

$\left(\dfrac{2 j^{3}}{3 k}\right)^{4}$

Zoezi$\PageIndex{40}$

$\left(\dfrac{3 m^{5}}{5 n}\right)^{3}$

Jibu

$\dfrac{27 m^{15}}{125 n^{3}}$

Zoezi$\PageIndex{41}$

$\left(\dfrac{3 c^{2}}{4 d^{6}}\right)^{3}$

Zoezi$\PageIndex{42}$

$\left(\dfrac{5 u^{7}}{2 v^{3}}\right)^{4}$

Jibu

$\dfrac{625 u^{28}}{16 v^{12}}$

Zoezi$\PageIndex{43}$

$\left(\dfrac{k^{2} k^{8}}{k^{3}}\right)^{2}$

Zoezi$\PageIndex{44}$

$\left(\dfrac{j^{2} j^{5}}{j^{4}}\right)^{3}$

Jibu

$j^{9}$

Zoezi$\PageIndex{45}$

$\dfrac{\left(t^{2}\right)^{5}\left(t^{4}\right)^{2}}{\left(t^{3}\right)^{7}}$

Zoezi$\PageIndex{46}$

$\dfrac{\left(q^{3}\right)^{6}\left(q^{2}\right)^{3}}{\left(q^{4}\right)^{8}}$

Jibu

$\dfrac{1}{q^{8}}$

Zoezi$\PageIndex{47}$

$\dfrac{\left(-2 p^{2}\right)^{4}\left(3 p^{4}\right)^{2}}{\left(-6 p^{3}\right)^{2}}$

Zoezi$\PageIndex{48}$

$\dfrac{\left(-2 k^{3}\right)^{2}\left(6 k^{2}\right)^{4}}{\left(9 k^{4}\right)^{2}}$

Jibu

64$k^{6}$

Zoezi$\PageIndex{49}$

$\dfrac{\left(-4 m^{3}\right)^{2}\left(5 m^{4}\right)^{3}}{\left(-10 m^{6}\right)^{3}}$

Zoezi$\PageIndex{50}$

$\dfrac{\left(-10 n^{2}\right)^{3}\left(4 n^{5}\right)^{2}}{\left(2 n^{8}\right)^{2}}$

Jibu

-4,000

Gawanya Monomials

Katika mazoezi yafuatayo, ugawanye monomials.

Zoezi$\PageIndex{51}$

56$b^{8} \div 7 b^{2}$

Zoezi$\PageIndex{52}$

63$\nu^{10} \div 9 v^{2}$

Jibu

7$v^{8}$

Zoezi$\PageIndex{53}$

$-88 y^{15} \div 8 y^{3}$

Zoezi$\PageIndex{54}$

$-72 u^{12} \div 12 u^{4}$

Jibu

$-6 u^{8}$

Zoezi$\PageIndex{55}$

$\dfrac{45 a^{6} b^{8}}{-15 a^{10} b^{2}}$

Zoezi$\PageIndex{56}$

$\dfrac{54 x^{9} y^{3}}{-18 x^{6} y^{15}}$

Jibu

$-\dfrac{3 x^{3}}{y^{12}}$

Zoezi$\PageIndex{57}$

$\dfrac{15 r^{4} s^{9}}{18 r^{9} s^{2}}$

Zoezi$\PageIndex{58}$

$\dfrac{20 m^{8} n^{4}}{30 m^{5} n^{9}}$

Jibu

$\dfrac{-2 m^{3}}{3 n^{5}}$

Zoezi$\PageIndex{59}$

$\dfrac{18 a^{4} b^{8}}{-27 a^{9} b^{5}}$

Zoezi$\PageIndex{60}$

$\dfrac{45 x^{5} y^{9}}{-60 x^{8} y^{6}}$

Jibu

$\dfrac{-3 y^{3}}{4 x^{3}}$

Zoezi$\PageIndex{61}$

$\dfrac{64 q^{11} r^{9} s^{3}}{48 q^{6} r^{8} s^{5}}$

Zoezi$\PageIndex{62}$

$\dfrac{65 a^{10} b^{8} c^{5}}{42 a^{7} b^{6} c^{8}}$

Jibu

$\dfrac{65 a^{3} b^{2}}{42 c^{3}}$

Zoezi$\PageIndex{63}$

$\dfrac{\left(10 m^{5} n^{4}\right)\left(5 m^{3} n^{6}\right)}{25 m^{7} n^{5}}$

Zoezi$\PageIndex{64}$

$\dfrac{\left(-18 p^{4} q^{7}\right)\left(-6 p^{3} q^{8}\right)}{-36 p^{12} q^{10}}$

Jibu

$\dfrac{-3 q^{5}}{p^{5}}$

Zoezi$\PageIndex{65}$

$\dfrac{\left(6 a^{4} b^{3}\right)\left(4 a b^{5}\right)}{\left(12 a^{2} b\right)\left(a^{3} b\right)}$

Zoezi$\PageIndex{66}$

$\dfrac{\left(4 u^{2} v^{5}\right)\left(15 u^{3} v\right)}{\left(12 u^{3} v\right)\left(u^{4} v\right)}$

Jibu

$\dfrac{5 v^{4}}{u^{2}}$

Mazoezi ya mchanganyiko

Zoezi$\PageIndex{67}$

1. $24 a^{5}+2 a^{5}$
2. $24 a^{5}-2 a^{5}$
3. 24$a^{5} \cdot 2 a^{5}$
4. 24$a^{5} \div 2 a^{5}$

Zoezi$\PageIndex{68}$

1. $15 n^{10}+3 n^{10}$
2. $15 n^{10}-3 n^{10}$
3. 15$n^{10} \cdot 3 n^{10}$
4. 15$n^{10} \div 3 n^{10}$

Jibu

1. 18$n^{10}$
2. 12$n^{10}$
3. 45$n^{20}$
4. 5

Zoezi$\PageIndex{69}$

1. $p^{4} \cdot p^{6}$
2. $\left(p^{4}\right)^{6}$

Zoezi$\PageIndex{70}$

1. $q^{5} \cdot q^{3}$
2. $\left(q^{5}\right)^{3}$

Jibu

1. $q^{8}$
2. $q^{15}$

Zoezi$\PageIndex{71}$

1. $\dfrac{y^{3}}{y}$
2. $\dfrac{y}{y^{3}}$

Zoezi$\PageIndex{72}$

1. $\dfrac{z^{6}}{z^{5}}$
2. $\dfrac{z^{5}}{z^{6}}$

Jibu

1. z
2. $\dfrac{1}{z}$

Zoezi$\PageIndex{73}$

$\left(8 x^{5}\right)(9 x) \div 6 x^{3}$

Zoezi$\PageIndex{74}$

$(4 y)\left(12 y^{7}\right) \div 8 y^{2}$

Jibu

6$y^{6}$

Zoezi$\PageIndex{75}$

$\dfrac{27 a^{7}}{3 a^{3}}+\dfrac{54 a^{9}}{9 a^{5}}$

Zoezi$\PageIndex{76}$

$\dfrac{32 c^{11}}{4 c^{5}}+\dfrac{42 c^{9}}{6 c^{3}}$

Jibu

15$c^{6}$

Zoezi$\PageIndex{77}$

$\dfrac{32 y^{5}}{8 y^{2}}-\dfrac{60 y^{10}}{5 y^{7}}$

Zoezi$\PageIndex{78}$

$\dfrac{48 x^{6}}{6 x^{4}}-\dfrac{35 x^{9}}{7 x^{7}}$

Jibu

3$x^{2}$

Zoezi$\PageIndex{79}$

$\dfrac{63 r^{6} s^{3}}{9 r^{4} s^{2}}-\dfrac{72 r^{2} s^{2}}{6 s}$

Zoezi$\PageIndex{80}$

$\dfrac{56 y^{4} z^{5}}{7 y^{3} z^{3}}-\dfrac{45 y^{2} z^{2}}{5 y}$

Jibu

$-y z^{2}$

kila siku Math

Zoezi$\PageIndex{81}$

Kumbukumbu Megabyte moja ni takriban$10^6$ bytes. Gigabyte moja ni takriban$10^9$ bytes. Ni megabytes ngapi katika gigabyte moja?

Zoezi$\PageIndex{82}$

Kumbukumbu Gigabyte moja ni takriban$10^9$ bytes. Terabyte moja ni takriban$10^12$ bytes. Ni gigabytes ngapi katika terabyte moja?

Jibu

$10^{3}$

Mazoezi ya kuandika

Zoezi$\PageIndex{83}$

Jennifer anadhani quotient$\dfrac{a^{24}}{a^{6}}$ simplifies kwa$a^{4} .$ nini ni makosa na hoja yake?

Zoezi$\PageIndex{84}$

Maurice simplifies quotient$\dfrac{d^{7}}{d}$ kwa kuandika$\dfrac{\not{d}^7}{\not{d}}=7 .$ Ni nini kibaya na hoja yake?

Jibu

Majibu yatatofautiana.

Zoezi$\PageIndex{85}$

Wakati Drake kilichorahisishwa$-3^{0}$ na$(-3)^{0}$ alipata jibu sawa. Eleza jinsi ya kutumia Utaratibu wa Uendeshaji kwa usahihi hutoa majibu
tofauti.

Zoezi$\PageIndex{86}$

Robert anadhani$x^{0}$ simplifies kwa 0. Ungesema nini kumshawishi Robert yeye ni makosa?

Jibu

Majibu yatatofautiana.

Self Check

Baada ya kukamilisha mazoezi, tumia orodha hii ili kutathmini ujuzi wako wa malengo ya sehemu hii.

b Kwa kiwango cha 1-10, ungewezaje kupima ujuzi wako wa sehemu hii kwa kuzingatia majibu yako kwenye orodha? Unawezaje kuboresha hii?