Sura ya 6 Mazoezi Mapitio

Sura ya 6 Mazoezi Mapitio

Kuongeza na Ondoa Polynomials

Kutambua Polynomials, Monomials, Binomials na Trinomials

Katika mazoezi yafuatayo, onyesha kama kila moja ya polynomials zifuatazo ni monomial, binomial, trinomial, au polynomial nyingine.

Zoezi$\PageIndex{1}$

1. $11 c^{4}-23 c^{2}+1$
2. $9 p^{3}+6 p^{2}-p-5$
3. $\frac{3}{7} x+\frac{5}{14}$
4. 10
5. 2y-12

Zoezi$\PageIndex{2}$

1. $a^{2}-b^{2}$
2. 24$d^{3}$
3. $x^{2}+8 x-10$
4. $m^{2} n^{2}-2 m n+6$
5. $7 y^{3}+y^{2}-2 y-4$

Jibu

1. binomial
2. monomial
3. ya trinomial
4. ya trinomial
5. nyingine polynomial

Kuamua Shahada ya Polynomials

Katika mazoezi yafuatayo, tambua kiwango cha kila polynomial.

Zoezi$\PageIndex{3}$

1. $3 x^{2}+9 x+10$
2. 14$a^{2} b c$
3. 6y+1
4. $n^{3}-4 n^{2}+2 n-8$
5. 19-19

Zoezi$\PageIndex{4}$

1. $5 p^{3}-8 p^{2}+10 p-4$
2. $-20 q^{4}$
3. $x^{2}+6 x+12$
4. $23 r^{2} s^{2}-4 r s+5$
5. 100

Jibu

1. 3
2. 4
3. 2
4. 4
5. 0

Kuongeza na Ondoa Monomials

Katika mazoezi yafuatayo, ongeza au uondoe monomials.

Zoezi$\PageIndex{5}$

$5 y^{3}+8 y^{3}$

Zoezi$\PageIndex{6}$

$-14 k+19 k$

Jibu

5k

Zoezi$\PageIndex{7}$

12q (-6q)

Zoezi$\PageIndex{8}$

-9c—18c

Jibu

-27c

Zoezi$\PageIndex{9}$

12x-4y-9x

Zoezi$\PageIndex{2}$

$3 m^{2}+7 n^{2}-3 m^{2}$

Jibu

7$n^{2}$

Zoezi$\PageIndex{3}$

$6 x^{2} y-4 x+8 x y^{2}$

Zoezi$\PageIndex{4}$

13a+b

Jibu

13a+b

Kuongeza na Ondoa Polynomials

Katika mazoezi yafuatayo, ongeza au uondoe polynomials.

Zoezi$\PageIndex{5}$

$\left(5 x^{2}+12 x+1\right)+\left(6 x^{2}-8 x+3\right)$

Zoezi$\PageIndex{6}$

$\left(9 p^{2}-5 p+3\right)+\left(4 p^{2}-4\right)$

Jibu

$13 p^{2}-5 p-1$

Zoezi$\PageIndex{7}$

$\left(10 m^{2}-8 m-1\right)-\left(5 m^{2}+m-2\right)$

Zoezi$\PageIndex{8}$

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

Jibu

$7 y^{2}-9 y+4$

Zoezi$\PageIndex{9}$

Ondoa
$\left(3 s^{2}+10\right)$ kutoka$\left(15 s^{2}-2 s+8\right)$

Zoezi$\PageIndex{10}$

Kupata jumla ya$\left(a^{2}+6 a+9\right)$ na$\left(5 a^{3}-7\right)$

Jibu

$5 a^{3}+a^{2}+6 a+2$

Tathmini Polynomial kwa Thamani iliyotolewa ya Variable

Katika mazoezi yafuatayo, tathmini kila polynomial kwa thamani iliyotolewa.

Zoezi$\PageIndex{11}$

Tathmini$3 y^{2}-y+1$ wakati:

1. y=5
2. y=-1
3. y=0

Zoezi$\PageIndex{12}$

Tathmini 10-12x wakati:

1. x=3
2. x=0
3. x=-1

Jibu

1. -26
2. 10
3. 22

Zoezi$\PageIndex{13}$

Randee matone jiwe mbali 200 mguu juu mwamba katika bahari. Polynomial$-16 t^{2}+200$ inatoa urefu wa jiwe t sekunde baada ya kushuka kutoka mwamba. Pata urefu baada ya sekunde t=3.

Zoezi$\PageIndex{14}$

Mtengenezaji wa wasemaji wa sauti ya stereo amegundua kwamba mapato yaliyopatikana kutokana na kuuza wasemaji kwa gharama ya dola p kila mmoja hutolewa na polynomial$-4 p^{2}+460 p$. Kupata mapato kupokea wakati p=75 dola.

Jibu

12,000

Tumia Mali ya kuzidisha ya Watazamaji

Kurahisisha Maneno na Watazamaji

Katika mazoezi yafuatayo, kurahisisha.

Zoezi$\PageIndex{15}$

$10^{4}$

Zoezi$\PageIndex{16}$

$17^{1}$

Jibu

17

Zoezi$\PageIndex{17}$

$\left(\frac{2}{9}\right)^{2}$

Zoezi$\PageIndex{18}$

$(0.5)^{3}$

Jibu

0.125

Zoezi$\PageIndex{19}$

$(-2)^{6}$

Zoezi$\PageIndex{20}$

$-2^{6}$

Jibu

-64

Kurahisisha Maneno Kutumia Mali ya Bidhaa kwa Watazamaji

Katika mazoezi yafuatayo, kurahisisha kila kujieleza.

Zoezi$\PageIndex{21}$

$x^{4} \cdot x^{3}$

Zoezi$\PageIndex{22}$

$p^{15} \cdot p^{16}$

Jibu

$p^{31}$

Zoezi$\PageIndex{23}$

$4^{10} \cdot 4^{6}$

Zoezi$\PageIndex{24}$

8$\cdot 8^{5}$

Jibu

$8^{6}$

Zoezi$\PageIndex{25}$

$n \cdot n^{2} \cdot n^{4}$

Zoezi$\PageIndex{26}$

$y^{c} \cdot y^{3}$

Jibu

$y^{c+3}$

Kurahisisha Maneno Kutumia Mali ya Nguvu kwa Wasanii

Katika mazoezi yafuatayo, kurahisisha kila kujieleza.

Zoezi$\PageIndex{27}$

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

Zoezi$\PageIndex{28}$

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

Jibu

$5^{6}$

Zoezi$\PageIndex{29}$

$\left(y^{4}\right)^{x}$

Zoezi$\PageIndex{30}$

$\left(3^{r}\right)^{s}$

Jibu

$3^{r s}$

Kurahisisha Maneno Kutumia Bidhaa kwa Mali ya Nguvu

Katika mazoezi yafuatayo, kurahisisha kila kujieleza.

Zoezi$\PageIndex{31}$

$(4 a)^{2}$

Zoezi$\PageIndex{32}$

$(-5 y)^{3}$

Jibu

$-125 y^{3}$

Zoezi$\PageIndex{33}$

$(2 m n)^{5}$

Zoezi$\PageIndex{34}$

$(10 x y z)^{3}$

Jibu

1000$x^{3} y^{3} z^{3}$

Kurahisisha Maneno kwa kutumia Mali kadhaa

Katika mazoezi yafuatayo, kurahisisha kila kujieleza.

Zoezi$\PageIndex{35}$

$\left(p^{2}\right)^{5} \cdot\left(p^{3}\right)^{6}$

Zoezi$\PageIndex{36}$

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

Jibu

64$a^{9} b^{6}$

Zoezi$\PageIndex{37}$

$(5 x)^{2}(7 x)$

Zoezi$\PageIndex{38}$

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

Jibu

48$q^{14}$

Zoezi$\PageIndex{39}$

$\left(\frac{1}{3} x^{2}\right)^{2}\left(\frac{1}{2} x\right)^{3}$

Zoezi$\PageIndex{40}$

$\left(\frac{2}{5} m^{2} n\right)^{3}$

Jibu

$\frac{8}{125} m^{6} n^{3}$

Kuzidisha Monomials

Katika mazoezi yafuatayo 8, kuzidisha monomials.

Zoezi$\PageIndex{41}$

$\left(-15 x^{2}\right)\left(6 x^{4}\right)$

Zoezi$\PageIndex{42}$

$\left(-9 n^{7}\right)(-16 n)$

Jibu

144$n^{8}$

Zoezi$\PageIndex{43}$

$\left(7 p^{5} q^{3}\right)\left(8 p q^{9}\right)$

Zoezi$\PageIndex{44}$

$\left(\frac{5}{9} a b^{2}\right)\left(27 a b^{3}\right)$

Jibu

15$a^{2} b^{5}$

Kuzidisha Polynomials

Kuzidisha Polynomial na Monomial

Katika mazoezi yafuatayo, ongeze.

Zoezi$\PageIndex{45}$

7 (a+9)

Zoezi$\PageIndex{46}$

-4 (y+13)

Jibu

-4y-52

Zoezi$\PageIndex{47}$

-5 (r-1)

Zoezi$\PageIndex{48}$

p (p+3)

Jibu

$p^{2}+3 p$

Zoezi$\PageIndex{49}$

-m (m+15)

Zoezi$\PageIndex{50}$

-6u (2u+7)

Jibu

$-12 u^{2}-42 u$

Zoezi$\PageIndex{51}$

9$\left(b^{2}+6 b+8\right)$

Zoezi$\PageIndex{52}$

3$q^{2}\left(q^{2}-7 q+6\right) 3$

Jibu

$3 q^{4}-21 q^{3}+18 q^{2}$

Zoezi$\PageIndex{53}$

$(5 z-1) z$

Zoezi$\PageIndex{54}$

$(b-4) \cdot 11$

Jibu

11b-44

Kuzidisha Binomial na Binomial

Katika mazoezi yafuatayo, kuzidisha binomials kutumia:

1. Mali ya Kusambaza,
2. njia ya FOIL,
3. Njia ya Wima.

Zoezi$\PageIndex{55}$

(x-4) (x+10)

Zoezi$\PageIndex{56}$

(6y-7) (2y-5)

Jibu

1. $12 y^{2}-44y+35$
2. $12 y^{2}-44y+35$
3. $12 y^{2}-44y+35$

Katika mazoezi yafuatayo, kuzidisha binomials. Tumia njia yoyote.

Zoezi$\PageIndex{57}$

(x+3) (x+9)

Zoezi$\PageIndex{58}$

(y-4) (y-8)

Jibu

$y^{2}-12 y+32$

Zoezi$\PageIndex{59}$

(p-7) (p+4)

Zoezi$\PageIndex{60}$

(q+16) (q-3)

Jibu

$q^{2}+13 q-48$

Zoezi$\PageIndex{61}$

(5m-8) (12m+1)

Zoezi$\PageIndex{62}$

$\left(u^{2}+6\right)\left(u^{2}-5\right)$

Jibu

$u^{4}+u^{2}-30$

Zoezi$\PageIndex{63}$

(9x-y) (6x-5)

Zoezi$\PageIndex{64}$

(8mn+3) (2mn-1)

Jibu

$16 m^{2} n^{2}-2 m n-3$

Kuzidisha Trinomial na Binomial

Katika mazoezi yafuatayo, kuzidisha kutumia

1. Mali ya Kusambaza,
2. Njia ya Wima.

Zoezi$\PageIndex{65}$

$(n+1)\left(n^{2}+5 n-2\right)$

Zoezi$\PageIndex{66}$

$(3 x-4)\left(6 x^{2}+x-10\right)$

Jibu

1. $18 x^{3}-21 x^{2}-34 x+40$
2. $18 x^{3}-21 x^{2}-34 x+40$

Katika mazoezi yafuatayo, ongeze. Tumia njia yoyote.

Zoezi$\PageIndex{67}$

$(y-2)\left(y^{2}-8 y+9\right)$

Zoezi$\PageIndex{68}$

$(7 m+1)\left(m^{2}-10 m-3\right)$

Jibu

$7 m^{3}-69 m^{2}-31 m-3$

Bidhaa Maalum

Mraba Binomial Kutumia Mipangilio ya Mraba ya Binomial

Katika mazoezi yafuatayo, mraba kila binomial kwa kutumia Pattern ya Mraba ya Binomial.

Zoezi$\PageIndex{69}$

$(c+11)^{2}$

Zoezi$\PageIndex{70}$

$(q-15)^{2}$

Jibu

$q^{2}-30 q+225$

Zoezi$\PageIndex{71}$

$\left(x+\frac{1}{3}\right)^{2}$

Zoezi$\PageIndex{72}$

$(8 u+1)^{2}$

Jibu

$64 u^{2}+16 u+1$

Zoezi$\PageIndex{73}$

$\left(3 n^{3}-2\right)^{2}$

Zoezi$\PageIndex{74}$

$(4 a-3 b)^{2}$

Jibu

$16 a^{2}-24 a b+9 b^{2}$

Kuzidisha conjugates Kutumia Bidhaa ya Conjugates Pattern

Katika mazoezi yafuatayo, kuzidisha kila jozi ya conjugates kwa kutumia Bidhaa ya Conjugates Pattern.

Zoezi$\PageIndex{75}$

(s-7) (s+7)

Zoezi$\PageIndex{76}$

$\left(y+\frac{2}{5}\right)\left(y-\frac{2}{5}\right)$

Jibu

$y^{2}-\frac{4}{25}$

Zoezi$\PageIndex{77}$

$(12 c+13)(12 c-13)$

Zoezi$\PageIndex{78}$

(6,1r) (6+r)

Jibu

$36-r^{2}$

Zoezi$\PageIndex{79}$

$\left(u+\frac{3}{4} v\right)\left(u-\frac{3}{4} v\right)$

Zoezi$\PageIndex{80}$

$\left(5 p^{4}-4 q^{3}\right)\left(5 p^{4}+4 q^{3}\right)$

Jibu

$25 p^{8}-16 q^{6}$

Tambua na Tumia Pattern maalum ya Bidhaa

Katika mazoezi yafuatayo, tafuta kila bidhaa.

Zoezi$\PageIndex{81}$

$(3 m+10)^{2}$

Zoezi$\PageIndex{82}$

(6a+11) (6a-11)

Jibu

$36 a^{2}-121$

Zoezi$\PageIndex{83}$

(5x+y) (x-5y)

Zoezi$\PageIndex{84}$

$\left(c^{4}+9 d\right)^{2}$

Jibu

$c^{8}+18 c^{4} d+81 d^{2}$

Zoezi$\PageIndex{85}$

$\left(p^{5}+q^{5}\right)\left(p^{5}-q^{5}\right)$

Zoezi$\PageIndex{86}$

$\left(a^{2}+4 b\right)\left(4 a-b^{2}\right)$

Jibu

$4 a^{3}+3 a^{2} b-4 b^{3}$

Kugawanya Monomials

Kurahisisha Maneno Kutumia Mali ya Quotient kwa Watazamaji

Katika mazoezi yafuatayo, kurahisisha.

Zoezi$\PageIndex{87}$

$\frac{u^{24}}{u^{6}}$

Zoezi$\PageIndex{88}$

$\frac{10^{25}}{10^{5}}$

Jibu

$10^{20}$

Zoezi$\PageIndex{89}$

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

Zoezi$\PageIndex{90}$

$\frac{v^{12}}{v^{48}}$

Jibu

$\frac{1}{v^{36}}$

Zoezi$\PageIndex{91}$

$\frac{x}{x^{5}}$

Zoezi$\PageIndex{92}$

$\frac{5}{5^{8}}$

Jibu

$\frac{1}{5^{7}}$

Kurahisisha Maneno na Zero Exponents

Katika mazoezi yafuatayo, kurahisisha.

Zoezi$\PageIndex{93}$

$75^{0}$

Zoezi$\PageIndex{94}$

$x^{0}$

Jibu

1

Zoezi$\PageIndex{95}$

$-12^{0}$

Zoezi$\PageIndex{96}$

$\left(-12^{0}\right)(-12)^{0}$

Jibu

1

Zoezi$\PageIndex{97}$

25$x^{0}$

Zoezi$\PageIndex{98}$

$(25 x)^{0}$

Jibu

1

Zoezi$\PageIndex{99}$

$19 n^{0}-25 m^{0}$

Zoezi$\PageIndex{100}$

$(19 n)^{0}-(25 m)^{0}$

Jibu

0

Kurahisisha Maneno Kutumia Quotient kwa Mali ya Nguvu

Katika mazoezi yafuatayo, kurahisisha.

Zoezi$\PageIndex{101}$

$\left(\frac{2}{5}\right)^{3}$

Zoezi$\PageIndex{102}$

$\left(\frac{m}{3}\right)^{4}$

Jibu

$\frac{m^{4}}{81}$

Zoezi$\PageIndex{103}$

$\left(\frac{r}{s}\right)^{8}$

Zoezi$\PageIndex{104}$

$\left(\frac{x}{2 y}\right)^{6}$

Jibu

$\frac{x^{6}}{64 y^{6}}$

Kurahisisha Maneno kwa kutumia Mali kadhaa

Katika mazoezi yafuatayo, kurahisisha.

Zoezi$\PageIndex{105}$

$\frac{\left(x^{3}\right)^{5}}{x^{9}}$

Zoezi$\PageIndex{106}$

$\frac{n^{10}}{\left(n^{5}\right)^{2}}$

Jibu

1

Zoezi$\PageIndex{107}$

$\left(\frac{q^{6}}{q^{8}}\right)^{3}$

Zoezi$\PageIndex{108}$

$\left(\frac{r^{8}}{r^{3}}\right)^{4}$

Jibu

$r^{20}$

Zoezi$\PageIndex{109}$

$\left(\frac{c^{2}}{d^{5}}\right)^{9}$

Zoezi$\PageIndex{110}$

$\left(\frac{3 x^{4}}{2 y^{2}}\right)^{5}$

Jibu

$\frac{343 x^{20}}{32 y^{10}}$

Zoezi$\PageIndex{111}$

$\left(\frac{v^{3} v^{9}}{v^{6}}\right)^{4}$

Zoezi$\PageIndex{112}$

$\frac{\left(3 n^{2}\right)^{4}\left(-5 n^{4}\right)^{3}}{\left(-2 n^{5}\right)^{2}}$

Jibu

$-\frac{10,125 n^{10}}{4}$

Kugawanya Monomials

Katika mazoezi yafuatayo, ugawanye monomials.

Zoezi$\PageIndex{113}$

$-65 y^{14} \div 5 y^{2}$

Zoezi$\PageIndex{114}$

$\frac{64 a^{5} b^{9}}{-16 a^{10} b^{3}}$

Jibu

$-\frac{4 b^{6}}{a^{5}}$

Zoezi$\PageIndex{115}$

$\frac{144 x^{15} y^{8} z^{3}}{18 x^{10} y^{2} z^{12}}$

Zoezi$\PageIndex{116}$

$\frac{\left(8 p^{6} q^{2}\right)\left(9 p^{3} q^{5}\right)}{16 p^{8} q^{7}}$

Jibu

$\frac{9 p}{2}$

Gawanya Polynomials

Gawanya Polynomial na Monomial

Katika mazoezi yafuatayo, kugawanya kila polynomial na monomial.

Zoezi$\PageIndex{117}$

$\frac{42 z^{2}-18 z}{6}$

Zoezi$\PageIndex{118}$

$\left(35 x^{2}-75 x\right) \div 5 x$

Jibu

7x-15

Zoezi$\PageIndex{119}$

$\frac{81 n^{4}+105 n^{2}}{-3}$

Zoezi$\PageIndex{120}$

$\frac{550 p^{6}-300 p^{4}}{10 p^{3}}$

Jibu

$55 p^{3}-30 p$

Zoezi$\PageIndex{121}$

$\left(63 x y^{3}+56 x^{2} y^{4}\right) \div(7 x y)$

Zoezi$\PageIndex{122}$

$\frac{96 a^{5} b^{2}-48 a^{4} b^{3}-56 a^{2} b^{4}}{8 a b^{2}}$

Jibu

$12 a^{4}-6 a^{3} b-7 a b^{2}$

Zoezi$\PageIndex{123}$

$\frac{57 m^{2}-12 m+1}{-3 m}$

Zoezi$\PageIndex{124}$

$\frac{105 y^{5}+50 y^{3}-5 y}{5 y^{3}}$

Jibu

$21 y^{2}+10-\frac{1}{y^{2}}$

Gawanya Polynomial na Binomial

Katika mazoezi yafuatayo, kugawanya kila polynomial na binomial.

Zoezi$\PageIndex{125}$

$\left(k^{2}-2 k-99\right) \div(k+9)$

Zoezi$\PageIndex{126}$

$\left(v^{2}-16 v+64\right) \div(v-8)$

Jibu

v-8

Zoezi$\PageIndex{127}$

$\left(3 x^{2}-8 x-35\right) \div(x-5)$

Zoezi$\PageIndex{128}$

$\left(n^{2}-3 n-14\right) \div(n+3)$

Jibu

$n-6+\frac{4}{n+3}$

Zoezi$\PageIndex{129}$

$\left(4 m^{3}+m-5\right) \div(m-1)$

Zoezi$\PageIndex{130}$

$\left(u^{3}-8\right) \div(u-2)$

Jibu

$u^{2}+2 u+4$

Integer Exponents na Nukuu ya kisayansi

Tumia Ufafanuzi wa Mtazamaji Mbaya

Katika mazoezi yafuatayo, kurahisisha.

Zoezi$\PageIndex{131}$

$9^{-2}$

Zoezi$\PageIndex{132}$

$(-5)^{-3}$

Jibu

$-\frac{1}{125}$

Zoezi$\PageIndex{133}$

3$\cdot 4^{-3}$

Zoezi$\PageIndex{134}$

$(6 u)^{-3}$

Jibu

$\frac{1}{216 u^{3}}$

Zoezi$\PageIndex{135}$

$\left(\frac{2}{5}\right)^{-1}$

Zoezi$\PageIndex{136}$

$\left(\frac{3}{4}\right)^{-2}$

Jibu

$\frac{16}{9}$

Kurahisisha Maneno na Exponents Integer

Katika mazoezi yafuatayo, kurahisisha.

Zoezi$\PageIndex{137}$

$p^{-2} \cdot p^{8}$

Zoezi$\PageIndex{138}$

$q^{-6} \cdot q^{-5}$

Jibu

$\frac{1}{q^{11}}$

Zoezi$\PageIndex{139}$

$\left(c^{-2} d\right)\left(c^{-3} d^{-2}\right)$

Zoezi$\PageIndex{140}$

$\left(y^{8}\right)^{-1}$

Jibu

$\frac{1}{y^{8}}$

Zoezi$\PageIndex{141}$

$\left(q^{-4}\right)^{-3}$

Zoezi$\PageIndex{142}$

$\frac{a^{8}}{a^{12}}$

Jibu

$\frac{1}{a^{4}}$

Zoezi$\PageIndex{143}$

$\frac{n^{5}}{n^{-4}}$

Zoezi$\PageIndex{144}$

$\frac{r^{-2}}{r^{-3}}$

Jibu

r

Badilisha kutoka Nukuu ya Decimal hadi Nukuu ya kisayansi

Katika mazoezi yafuatayo, weka kila nambari katika maelezo ya kisayansi.

Zoezi$\PageIndex{145}$

8,500,000

Zoezi$\PageIndex{146}$

0.00429

Jibu

$4.29 \times 10^{-3}$

Zoezi$\PageIndex{147}$

Unene wa dime ni kuhusu inchi 0.053.

Zoezi$\PageIndex{148}$

Mwaka 2015, idadi ya wakazi duniani ilikuwa watu wapatao 7,200,000,000.

Jibu

$7.2 \times 10^{9}$

Badilisha Nukuu ya kisayansi kwa Fomu ya Decima

Katika mazoezi yafuatayo, kubadilisha kila nambari kwa fomu ya decimal.

Zoezi$\PageIndex{149}$

$3.8 \times 10^{5}$

Zoezi$\PageIndex{150}$

$1.5 \times 10^{10}$

Jibu

15,000,000,000

Zoezi$\PageIndex{151}$

$9.1 \times 10^{-7}$

Zoezi$\PageIndex{152}$

$5.5 \times 10^{-1}$

Jibu

0.55

Kuzidisha na Gawanya Kutumia Notation ya

Katika mazoezi yafuatayo, kuzidisha na kuandika jibu lako kwa fomu ya decimal.

Zoezi$\PageIndex{153}$

$\left(2 \times 10^{5}\right)\left(4 \times 10^{-3}\right)$

Zoezi$\PageIndex{154}$

$\left(3.5 \times 10^{-2}\right)\left(6.2 \times 10^{-1}\right)$

Jibu

0.2017

Katika mazoezi yafuatayo, ugawanye na uandike jibu lako kwa fomu ya decimal.

Zoezi$\PageIndex{155}$

$\frac{8 \times 10^{5}}{4 \times 10^{-1}}$

Zoezi$\PageIndex{156}$

$\frac{9 \times 10^{-5}}{3 \times 10^{2}}$

Jibu

0.00003

Sura ya Mazoezi mtihani

Zoezi$\PageIndex{1}$

Kwa polynomial$10 x^{4}+9 y^{2}-1$
ⓐ Je, ni monomial, binomial, au trinomial?
ⓑ Shahada yake ni nini?

Katika mazoezi yafuatayo, kurahisisha kila kujieleza.

Zoezi$\PageIndex{2}$

$\left(12 a^{2}-7 a+4\right)+\left(3 a^{2}+8 a-10\right)$

Jibu

$15 a^{2}+a-6$

Zoezi$\PageIndex{3}$

$\left(9 p^{2}-5 p+1\right)-\left(2 p^{2}-6\right)$

Zoezi$\PageIndex{4}$

$\left(-\frac{2}{5}\right)^{3}$

Jibu

$-\frac{8}{125}$

Zoezi$\PageIndex{5}$

$u \cdot u^{4}$

Zoezi$\PageIndex{6}$

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

Jibu

16$a^{6} b^{10}$

Zoezi$\PageIndex{7}$

$\left(-9 r^{4} s^{5}\right)\left(4 r s^{7}\right)$

Zoezi$\PageIndex{8}$

3$k\left(k^{2}-7 k+13\right)$

Jibu

$3 k^{3}-21 k^{2}+39 k$

Zoezi$\PageIndex{9}$

$(m+6)(m+12)$

Zoezi$\PageIndex{10}$

(v-9) (9v-5)

Jibu

$9 v^{2}-86 v+45$

Zoezi$\PageIndex{11}$

(4c-11) (3c-8)

Zoezi$\PageIndex{12}$

$(n-6)\left(n^{2}-5 n+4\right)$

Jibu

$n^{3}-11 n^{2}+34 n-24$

Zoezi$\PageIndex{13}$

$(2 x-15 y)(5 x+7 y)$

Zoezi$\PageIndex{14}$

$(7 p-5)(7 p+5)$

Jibu

$49 p^{2}-25$

Zoezi$\PageIndex{15}$

$(9 v-2)^{2}$

Zoezi$\PageIndex{16}$

$\frac{3^{8}}{3^{10}}$

Jibu

$\frac{1}{9}$

Zoezi$\PageIndex{17}$

$\left(\frac{m^{4} \cdot m}{m^{3}}\right)^{6}$

Zoezi$\PageIndex{18}$

$\left(87 x^{15} y^{3} z^{22}\right)^{0}$

Jibu

1

Zoezi$\PageIndex{19}$

$\frac{80 c^{8} d^{2}}{16 c d^{10}}$

Zoezi$\PageIndex{20}$

$\frac{12 x^{2}+42 x-6}{2 x}$

Jibu

$6 x+21-\frac{3}{x}$

Zoezi$\PageIndex{21}$

$\left(70 x y^{4}+95 x^{3} y\right) \div 5 x y$

Zoezi$\PageIndex{22}$

$\frac{64 x^{3}-1}{4 x-1}$

Jibu

$16 x^{2}+4 x+1$

Zoezi$\PageIndex{23}$

$\left(y^{2}-5 y-18\right) \div(y+3)$

Zoezi$\PageIndex{24}$

$5^{-2}$

Jibu

$\frac{1}{25}$

Zoezi$\PageIndex{25}$

$(4 m)^{-3}$

Zoezi$\PageIndex{26}$

$q^{-4} \cdot q^{-5}$

Jibu

$\frac{1}{q^{9}}$

Zoezi$\PageIndex{27}$

$\frac{n^{-2}}{n^{-10}}$

Zoezi$\PageIndex{28}$

Geuza 83,000,000 kwa nukuu ya kisayansi.

Jibu

$8.3 \times 10^{7}$

Zoezi$\PageIndex{29}$

Badilisha$6.91 \times 10^{-5}$ kwenye fomu ya decimal.

Katika mazoezi yafuatayo, kurahisisha, na uandike jibu lako kwa fomu ya decimal.

Zoezi$\PageIndex{30}$

$\left(3.4 \times 10^{9}\right)\left(2.2 \times 10^{-5}\right)$

Jibu

74,800

Zoezi$\PageIndex{31}$

$\frac{8.4 \times 10^{-3}}{4 \times 10^{3}}$

Zoezi$\PageIndex{32}$

Helikopta ya kuruka kwenye urefu wa miguu 1000 hupungua mfuko wa uokoaji. Polynomial$-16 t^{2}+1000$ inatoa urefu wa mfuko t sekunde baada ya kushuka. Kupata urefu wakati t = 6 sekunde.

Jibu

Futi 424