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9.7E: Mazoezi

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    177438

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    Mazoezi hufanya kamili

    Rahisisha Maneno na Mizizi ya Juu

    Katika mazoezi yafuatayo, kurahisisha.

    Mfano\(\PageIndex{46}\)
    1. \(\sqrt[3]{216}\)
    2. \(\sqrt[4]{256}\)
    3. \(\sqrt[5]{32}\)
    Mfano\(\PageIndex{47}\)
    1. \(\sqrt[3]{27}\)
    2. \(\sqrt[4]{16}\)
    3. \(\sqrt[5]{243}\)
    Jibu
    1. 3
    2. 2
    3. 3
    Mfano\(\PageIndex{48}\)
    1. \(\sqrt[3]{512}\)
    2. \(\sqrt[4]{81}\)
    3. \(\sqrt[5]{1}\)
    Mfano\(\PageIndex{49}\)
    1. \(\sqrt[5]{125}\)
    2. \(\sqrt[4]{1296}\)
    3. \(\sqrt[5]{1024}\)
    Jibu
    1. 5
    2. 6
    3. 4
    Mfano\(\PageIndex{50}\)
    1. \(\sqrt[3]{−8}\)
    2. \(\sqrt[4]{−81}\)
    3. \(\sqrt[5]{−32}\)
    Mfano\(\PageIndex{51}\)
    1. \(\sqrt[3]{−64}\)
    2. \(\sqrt[4]{−16}\)
    3. \(\sqrt[5]{−243}\)
    Jibu
    1. -4
    2. si kweli
    3. 1-3
    Mfano\(\PageIndex{52}\)
    1. \(\sqrt[3]{−125}\)
    2. \(\sqrt[4]{−1296}\)
    3. \(\sqrt[5]{−1024}\)
    Mfano\(\PageIndex{53}\)
    1. \(\sqrt[3]{−512}\)
    2. \(\sqrt[4]{−81}\)
    3. \(\sqrt[5]{−1}\)
    Jibu
    1. -8
    2. si idadi halisi
    3. -1
    Mfano\(\PageIndex{54}\)
    1. \(\sqrt[5]{u^5}\)
    2. \(\sqrt[8]{v^8}\)
    Mfano\(\PageIndex{55}\)
    1. \(\sqrt[3]{a^3}\)

    .

    Jibu
    1. a
    2. |b|
    Mfano\(\PageIndex{56}\)
    1. \(\sqrt[4]{y^4}\)
    2. \(\sqrt[7]{m^7}\)
    Mfano\(\PageIndex{57}\)
    1. \(\sqrt[8]{k^8}\)
    2. \(\sqrt[6]{p^6}\)
    Jibu
    1. |k|
    2. p
    Mfano\(\PageIndex{58}\)
    1. \(\sqrt[3]{x^9}\)
    2. \(\sqrt[4]{y^{12}}\)
    Mfano\(\PageIndex{59}\)
    1. \(\sqrt[5]{a^{10}}\)
    2. \(\sqrt[3]{b^{27}}\)
    Jibu
    1. \(a^2\)
    2. \(b^9\)
    Mfano\(\PageIndex{60}\)
    1. \(\sqrt[4]{m^8}\)
    2. \(\sqrt[5]{n^{20}}\)
    Mfano\(\PageIndex{61}\)
    1. \(\sqrt[6]{r^{12}}\)
    2. \(\sqrt[3]{s^{30}}\)
    Jibu
    1. \(r^2\)
    2. \(s^{10}\)
    Mfano\(\PageIndex{62}\)
    1. \(\sqrt[4]{16x^8}\)
    2. \(\sqrt[6]{64y^{12}}\)
    Mfano\(\PageIndex{63}\)
    1. \(\sqrt[3]{−8c^9}\)
    2. \(\sqrt[3]{125d^{15}}\)
    Jibu
    1. \(−2c^3\)
    2. \(5d^5\)
    Mfano\(\PageIndex{64}\)
    1. \(\sqrt[3]{216a^6}\)
    2. \(\sqrt[5]{32b^{20}}\)
    Mfano\(\PageIndex{65}\)
    1. \(\sqrt[7]{128r^{14}}\)
    2. \(\sqrt[4]{81s^{24}}\)
    Jibu
    1. \(2r^2\)
    2. \(3s^6\)

    Tumia Mali ya Bidhaa ili kurahisisha Maneno na Mizizi ya Juu

    Katika mazoezi yafuatayo, kurahisisha.

    Zoezi\(\PageIndex{66}\)
    1. \(\sqrt[3]{r^5}\)
    2. \(\sqrt[4]{s^{10}}\)
    Mfano\(\PageIndex{67}\)
    1. \(\sqrt[5]{u^7}\)
    2. \(\sqrt[6]{v^{11}}\)
    Jibu
    1. \(u\sqrt[5]{u^2}\)
    2. \(v\sqrt[6]{v^5}\)
    Mfano\(\PageIndex{68}\)
    1. \(\sqrt[4]{m^5}\)
    2. \(\sqrt[8]{n^{10}}\)
    Mfano\(\PageIndex{69}\)
    1. \(\sqrt[5]{p^8}\)
    2. \(\sqrt[3]{q^8}\)
    Jibu
    1. \(p\sqrt[5]{p^3}\)
    2. \(q^2\sqrt[3]{q^2}\)
    Mfano\(\PageIndex{70}\)
    1. \(\sqrt[4]{32}\)
    2. \(\sqrt[5]{64}\)
    Mfano\(\PageIndex{71}\)
    1. \(\sqrt[3]{625}\)
    2. \(\sqrt[6]{128}\)
    Jibu
    1. \(5\sqrt[3]{5}\)
    2. \(2\sqrt[6]{2}\)
    Mfano\(\PageIndex{72}\)
    1. \(\sqrt[6]{64}\)
    2. \(\sqrt[3]{256}\)
    Mfano\(\PageIndex{73}\)
    1. \(\sqrt[4]{3125}\)
    2. \(\sqrt[3]{81}\)
    Jibu
    1. \(5\sqrt[4]{5}\)
    2. \(3\sqrt[3]{3}\)
    Mfano\(\PageIndex{74}\)
    1. \(\sqrt[3]{108x^5}\)
    2. \(\sqrt[4]{48y^6}\)
    Mfano\(\PageIndex{75}\)
    1. \(\sqrt[5]{96a^7}\)
    2. \(\sqrt[3]{375b^4}\)
    Jibu
    1. \(2a\sqrt[5]{3a^2}\)
    2. \(5b\sqrt[3]{3b}\)
    Mfano\(\PageIndex{76}\)
    1. \(\sqrt[4]{405m^{10}}\)
    2. \(\sqrt[5]{160n^8}\)
    Mfano\(\PageIndex{77}\)
    1. \(\sqrt[3]{512p^5}\)
    2. \(\sqrt[4]{324q^7}\)
    Jibu
    1. \(8p\sqrt[3]{p^2}\)
    2. \(3q\sqrt[4]{4q^3}\)
    Mfano\(\PageIndex{78}\)
    1. \(\sqrt[3]{−864}\)
    2. \(\sqrt[4]{−256}\)
    Mfano\(\PageIndex{79}\)
    1. \(\sqrt[5]{−486}\)
    2. \(\sqrt[6]{−64}\)
    Jibu
    1. \(−3\sqrt[5]{2}\)
    2. si kweli
    Mfano\(\PageIndex{80}\)
    1. \(\sqrt[5]{−32}\)
    2. \(\sqrt[8]{−1}\)
    Mfano\(\PageIndex{81}\)
    1. \(\sqrt[3]{−8}\)
    2. \(\sqrt[4]{−16}\)
    Jibu
    1. -2
    2. si kweli
    Tumia Mali ya Quotient ili kurahisisha Maneno na Mizizi ya Juu

    Katika mazoezi yafuatayo, kurahisisha.

    Mfano\(\PageIndex{82}\)
    1. \(\sqrt[3]{\frac{p^{11}}{p^2}}\)
    2. \(\sqrt[4]{\frac{q^{17}}{q^{13}}}\)
    Mfano\(\PageIndex{83}\)
    1. \(\sqrt[5]{\frac{d^{12}}{d^7}}\)
    2. \(\sqrt[8]{\frac{m^{12}}{m^4}}\)
    Jibu
    1. d
    2. |m|
    Mfano\(\PageIndex{84}\)
    1. \(\sqrt[5]{\frac{u^{21}}{u^{11}}}\)
    2. \(\sqrt[6]{\frac{v^{30}}{v^{12}}}\)
    Mfano\(\PageIndex{85}\)
    1. \(\sqrt[3]{\frac{r^{14}}{r^5}}\)
    2. \(\sqrt[4]{\frac{c^{21}}{c^9}}\)
    Jibu
    1. \(r^2\)
    2. \(∣c^3∣\)
    Mfano\(\PageIndex{86}\)
    1. \(\frac{\sqrt[4]{64}}{\sqrt[4]{2}}\)
    2. \(\frac{\sqrt[5]{128x^8}}{\sqrt[5]{2x^2}}\)
    Mfano\(\PageIndex{87}\)
    1. \(\frac{\sqrt[3]{−625}}{\sqrt[3]{5}}\)
    2. \(\frac{\sqrt[4]{80m^7}}{\sqrt[4]{5m}}\)
    Jibu
    1. -5
    2. \(4m\sqrt[4]{m^2}\)
    Mfano\(\PageIndex{88}\)
    1. \(\sqrt[3]{\frac{1050}{2}}\)
    2. \(\sqrt[4]{\frac{486y^9}{2y^3}}\)
    Mfano\(\PageIndex{89}\)
    1. \(\sqrt[3]{\frac{162}{6}}\)
    2. \(\sqrt[4]{\frac{160r^{10}}{5r^3}}\)
    Jibu
    1. \(3\sqrt[3]{6}\)
    2. \(2|r|\sqrt[4]{2r^3}\)
    Mfano\(\PageIndex{90}\)
    1. \(\sqrt[3]{\frac{54a^8}{b^3}}\)
    2. \(\sqrt[4]{\frac{64c^5}{d^2}}\)
    Mfano\(\PageIndex{91}\)
    1. \(\sqrt[5]{\frac{96r^{11}}{s^{3}}}\)
    2. \(\sqrt[6]{\frac{128u^7}{v^3}}\)
    Jibu
    1. \(\frac{2r^2\sqrt[5]{3r}}{s^3}\)
    2. \(\frac{2u\sqrt[6]{2uv^3}}{v}\)
    Mfano\(\PageIndex{92}\)
    1. \(\sqrt[3]{\frac{81s^8}{t^3}}\)
    2. \(\sqrt[4]{\frac{64p^{15}}{q^{12}}}\)
    Mfano\(\PageIndex{93}\)
    1. \(\sqrt[3]{\frac{625u^{10}}{v^3}}\)
    2. \(\sqrt[4]{\frac{729c^{21}}{d^8}}\)
    Jibu
    1. \(\frac{5u^3\sqrt[3]{5u}}{v}\)
    2. \(\frac{3c^5\sqrt[4]{9c}}{d^2}\)
    Ongeza na Ondoa Mizizi ya Juu

    Katika mazoezi yafuatayo, kurahisisha.

    Mfano\(\PageIndex{94}\)
    1. \(\sqrt[7]{8p}+\sqrt[7]{8p}\)
    2. \(3\sqrt[3]{25}−\sqrt[3]{25}\)
    Mfano\(\PageIndex{95}\)
    1. \(\sqrt[3]{15q}+\sqrt[3]{15q}\)
    2. \(2\sqrt[4]{27}−6\sqrt[4]{27}\)
    Jibu
    1. \(2\sqrt[3]{15q}\)
    2. \(−4\sqrt[4]{27}\)
    Mfano\(\PageIndex{96}\)
    1. \(3\sqrt[5]{9x}+7\sqrt[5]{9x}\)
    2. \(8\sqrt[7]{3q}−2\sqrt[7]{3q}\)
    Mfano\(\PageIndex{97}\)

    1.

    .

    2.

    .

    Jibu

    1.

    .

    2.

    .

    Mfano\(\PageIndex{98}\)
    1. \(\sqrt[3]{81}−\sqrt[3]{192}\)
    2. \(\sqrt[4]{512}−\sqrt[4]{32}\)
    Mfano\(\PageIndex{99}\)
    1. \(\sqrt[3]{250}−\sqrt[3]{54}\)
    2. \(\sqrt[4]{243}−\sqrt[4]{1875}\)
    Jibu
    1. \(5\sqrt[3]{5}−3\sqrt[3]{2}\)
    2. \(−2\sqrt[4]{3}\)
    Mfano\(\PageIndex{100}\)
    1. \(\sqrt[3]{128}+\sqrt[3]{250}\)
    2. \(\sqrt[5]{729}+\sqrt[5]{96}\)
    Mfano\(\PageIndex{101}\)
    1. \(\sqrt[4]{243}+\sqrt[4]{1250}\)
    2. \(\sqrt[3]{2000}+\sqrt[3]{54}\)
    Jibu
    1. \(3\sqrt[4]{3}+5\sqrt[4]{2}\)
    2. \(13\sqrt[3]{2}\)
    Mfano\(\PageIndex{102}\)
    1. \(\sqrt[3]{64a^{10}}−\sqrt[3]{−216a^{12}}\)
    2. \(\sqrt[4]{486u^7}+\sqrt[4]{768u^3}\)
    Mfano\(\PageIndex{103}\)
    1. \(\sqrt[3]{80b^5}−\sqrt[3]{−270b^3}\)
    2. \(\sqrt[4]{160v^{10}}−\sqrt[4]{1280v^3}\)
    Jibu
    1. \(2b\sqrt[3]{10b^2}+3b\sqrt[3]{10}\)
    2. \(2v^2\sqrt[4]{10v^2}−4\sqrt[4]{5v^3}\)
    Mazoezi ya mchanganyiko

    Katika mazoezi yafuatayo, kurahisisha.

    Mfano\(\PageIndex{104}\)

    \(\sqrt[4]{16}\)

    Mfano\(\PageIndex{105}\)

    \(\sqrt[6]{64}\)

    Jibu

    2

    Mfano\(\PageIndex{106}\)

    \(\sqrt[3]{a^3}\)

    Mfano\(\PageIndex{107}\)

    .

    Jibu

    |b|

    Mfano\(\PageIndex{108}\)

    \(\sqrt[3]{−8c^9}\)

    Mfano\(\PageIndex{109}\)

    \(\sqrt[3]{125d^{15}}\)

    Jibu

    \(5d^5\)

    Mfano\(\PageIndex{110}\)

    \(\sqrt[3]{r^5}\)

    Mfano\(\PageIndex{111}\)

    \(\sqrt[4]{s^{10}}\)

    Jibu

    \(s^2\sqrt[4]{s^2}\)

    Mfano\(\PageIndex{112}\)

    \(\sqrt[3]{108x^5}\)

    Mfano\(\PageIndex{113}\)

    \(\sqrt[4]{48y^6}\)

    Jibu

    \(2y\sqrt[4]{3y^2}\)

    Mfano\(\PageIndex{114}\)

    \(\sqrt[5]{−486}\)

    Mfano\(\PageIndex{115}\)

    \(\sqrt[6]{−64}\)

    Jibu

    si kweli

    Mfano\(\PageIndex{116}\)

    \(\frac{\sqrt[4]{64}}{\sqrt[4]{2}}\)

    Mfano\(\PageIndex{117}\)

    \(\frac{\sqrt[5]{128x^8}}{\sqrt[5]{2x^2}}\)

    Jibu

    \(2x\sqrt[5]{2x}\)

    Mfano\(\PageIndex{118}\)

    \(\sqrt[5]{\frac{96r^{11}}{s^3}}\)

    Mfano\(\PageIndex{119}\)

    \(\sqrt[6]{\frac{128u^7}{v^3}}\)

    Jibu

    \(\frac{2u^3\sqrt[6]{2uv^3}}{v}\)

    Mfano\(\PageIndex{120}\)

    \(\sqrt[3]{81}−\sqrt[3]{192}\)

    Mfano\(\PageIndex{121}\)

    \(\sqrt[4]{512}−\sqrt[4]{32}\)

    Jibu

    \(4\sqrt[4]{2}\)

    Mfano\(\PageIndex{122}\)

    \(\sqrt[3]{64a^{10}}−\sqrt[3]{−216a^{12}}\)

    Mfano\(\PageIndex{123}\)

    \(\sqrt[4]{486u^7}+\sqrt[4]{768u^3}\)

    Jibu

    \(3u\sqrt[4]{6u^3}+4\sqrt[4]{3u^3}\)

    kila siku Math

    Mfano\(\PageIndex{124}\)

    Ukuaji wa idadi ya watu\(10·x^n\) mifano ya kujieleza ukuaji wa idadi ya watu mold baada ya vizazi n. Kulikuwa na spores 10 mwanzoni, na kila mmoja alikuwa na watoto wa x. Hivyo\(10·x^n\) ni idadi ya watoto katika kizazi cha tano. Katika kizazi cha tano kulikuwa na watoto 10,240. \(\sqrt[5]{\frac{10,240}{10}}\)Kurahisisha maneno ili kuamua idadi ya watoto wa kila spore.

    Mfano\(\PageIndex{125}\)

    Kuenea kwa virusi Maneno ya\(3·x^n\) kujieleza kuenea kwa virusi baada ya mizunguko n. Kulikuwa na watu watatu awali walioambukizwa na virusi, na kila mmoja wao aliambukizwa x watu. Hivyo\(3·x^4\) ni idadi ya watu walioambukizwa kwenye mzunguko wa nne. Katika mzunguko wa nne watu 1875 waliambukizwa. Kurahisisha usemi\(\sqrt[4]{\frac{1875}{3}}\) ili kuamua idadi ya watu kila mtu aliyeambukizwa.

    Jibu

    5

    Mazoezi ya kuandika

    Mfano\(\PageIndex{126}\)

    Eleza jinsi unavyojua hilo\(\sqrt[5]{x^{10}}=x^2\).

    Mfano\(\PageIndex{127}\)

    Eleza\(\sqrt[4]{−64}\) kwa nini si idadi halisi lakini\(\sqrt[3]{−64}\) ni.

    Jibu

    Majibu yanaweza kutofautiana.

    Self Check

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

    Jedwali hili lina nguzo nne na safu tano. Mstari wa kwanza unaandika kila safu: “Ninaweza...,” “Confidentaly,” “Kwa msaada fulani,” na “Hapana - Siipati!” Safu chini ya “naweza...,” safu inasoma, “kurahisisha maneno na mizizi ya hapa.,” “tumia mali ya bidhaa ili kurahisisha maneno na mizizi ya juu.”, “tumia mali ya quotient ili kurahisisha maneno na mizizi ya juu.”, “ongeza na uondoe mizizi ya juu.” Wengine wa safu chini ya nguzo ni tupu.

    ⓑ Orodha hii inakuambia nini kuhusu ujuzi wako wa sehemu hii? Ni hatua gani utachukua ili kuboresha?