9.8E: Mazoezi
- Page ID
- 177389
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Mazoezi hufanya kamili
Kurahisisha Maneno na\(a^{\frac{1}{n}}\)
Katika mazoezi yafuatayo, andika kama kujieleza kwa kiasi kikubwa.
- \(x^{\frac{1}{2}}\)
- \(y^{\frac{1}{3}}\)
- \(z^{\frac{1}{4}}\)
- \(r^{\frac{1}{2}}\)
- \(s^{\frac{1}{3}}\)
- \(t^{\frac{1}{4}}\)
- Jibu
-
- \(\sqrt{r}\)
- \(\sqrt[3]{s}\)
- \(\sqrt[4]{t}\)
- \(u^{\frac{1}{5}}\)
- \(v^{\frac{1}{9}}\)
- \(w^{\frac{1}{20}}\)
- \(g^{\frac{1}{7}}\)
- \(h^{\frac{1}{5}}\)
- \(j^{\frac{1}{25}}\)
- Jibu
-
- \(\sqrt[7]{g}\)
- \(\sqrt[5]{h}\)
- \(\sqrt[25]{j}\)
- \(−\sqrt[7]{x}\)
- \(\sqrt[9]{y}\)
- \(\sqrt[5]{f}\)
- \(\sqrt[8]{r}\)
- \(\sqrt[10]{s}\)
- \(\sqrt[4]{t}\)
- Jibu
-
- \(r^{\frac{1}{8}}\)
- \(s^{\frac{1}{10}}\)
- \(t^{\frac{1}{4}}\)
- \ (\ sqrt [3] {a}\
- \(\sqrt[12]{b}\)
- \(\sqrt{c}\)
- \(\sqrt[5]{u}\)
- \(\sqrt{v}\)
- Jibu
-
- \(u^{\frac{1}{5}}\)
- \(v^{\frac{1}{2}}\)
- \(w^{\frac{1}{16}}\)
- \(\sqrt[3]{7c}\)
- \(\sqrt[7]{12d}\)
- \(3\sqrt[4]{5f}\)
- \(\sqrt[4]{5x}\)
- \(\sqrt[8]{9y}\)
- \(7\sqrt[5]{3z}\)
- Jibu
-
- \((5x)^{\frac{1}{4}}\)
- \((9y)^{\frac{1}{8}}\)
- \(7(3z)^{\frac{1}{5}}\)
- \(\sqrt{21p}\)
- \(\sqrt[4]{8q}\)
- \(\sqrt[6]{436r}\)
- \(\sqrt[3]{25a}\)
- \(\sqrt{3b}\)
- Jibu
-
- \((25a)^{\frac{1}{3}}\)
- \((3b)^{\frac{1}{2}}\)
- \((40c)^{\frac{1}{10}}\)
Katika mazoezi yafuatayo, kurahisisha.
- \(81^{\frac{1}{2}}\)
- \(125^{\frac{1}{3}}\)
- \(64^{\frac{1}{2}}\)
- \(625^{\frac{1}{4}}\)
- \(243^{\frac{1}{5}}\)
- \(32^{\frac{1}{5}}\)
- Jibu
-
- 5
- 3
- 2
- \(16^{\frac{1}{4}}\)
- \(16^{\frac{1}{2}}\)
- \(3125^{\frac{1}{5}}\)
- \(216^{\frac{1}{3}}\)
- \(32^{\frac{1}{5}}\)
- \(81^{\frac{1}{4}}\)
- Jibu
-
- 6
- 2
- 3
- \((−216)^{\frac{1}{3}}\)
- \(−216^{\frac{1}{3}}\)
- \((216)^{−\frac{1}{3}}\)
- \((−243)^{\frac{1}{5}}\)
- \(−243^{\frac{1}{5}}\)
- \((243)^{−\frac{1}{5}}\)
- Jibu
-
- 1-3
- 1-3
- \(\frac{1}{3}\)
- \((−1)^{\frac{1}{3}}\)
- \(−1^{\frac{1}{3}}\)
- \((1)^{−\frac{1}{3}}\)
- \((−1000)^{\frac{1}{3}}\)
- \(−1000^{\frac{1}{3}}\)
- \((1000)^{−\frac{1}{3}}\)
- Jibu
-
- -10
- -10
- \ (\ frac {1} {10}
- \((−81)^{\frac{1}{4}}\)
- \(−81^{\frac{1}{4}}\)
- \((81)^{−\frac{1}{4}}\)
- \((−49)^{\frac{1}{2}}\)
- \(−49^{\frac{1}{2}}\)
- \((49)^{−\frac{1}{2}}\)
- Jibu
-
- si idadi halisi
- -7
- \(\frac{1}{7}\)
- \((−36)^{\frac{1}{2}}\)
- \(−36^{\frac{1}{2}}\)
- \((36)^{−\frac{1}{2}}\)
- \((−1)^{\frac{1}{4}}\)
- \((1)^{−\frac{1}{4}}\)
- \(−1^{\frac{1}{4}}\)
- Jibu
-
- si idadi halisi
- 1
- -1
- \((−100)^{\frac{1}{2}}\)
- \(−100^{\frac{1}{2}}\)
- \((100)^{−\frac{1}{2}}\)
- \((−32)^{\frac{1}{5}}\)
- \((243)^{−\frac{1}{5}}\)
- \(−125^{\frac{1}{3}}\)
- Jibu
-
- -2
- \(\frac{1}{3}\)
- -5
Kurahisisha Maneno na\(a^{\frac{m}{n}}\)
Katika mazoezi yafuatayo, andika kwa ufafanuzi wa busara.
- \(\sqrt{m^5}\)
- \(\sqrt[3]{n^2}\)
- \(\sqrt[4]{p^3}\)
- \(\sqrt[4]{r^7}\)
- \(\sqrt[5]{s^3}\)
- \(\sqrt[3]{t^7}\)
- Jibu
-
- \(r^{\frac{7}{4}}\)
- \(s^{\frac{3}{5}}\)
- \(t^{\frac{7}{3}}\)
- \(\sqrt[5]{u^2}\)
- \(\sqrt[5]{v^8}\)
- \(\sqrt[9]{w^4}\)
- \(\sqrt[3]{a}\)
- \(\sqrt[5]{b}\)
- \(\sqrt[3]{c^5}\)
- Jibu
-
- \(a^{\frac{1}{3}}\)
- \(b^{\frac{1}{5}}\)
- \(c^{\frac{5}{3}}\)
- \(16^{\frac{3}{2}}\)
- \(8^{\frac{2}{3}}\)
- \(10,000^{\frac{3}{4}}\)
- \(1000^{\frac{2}{3}}\)
- \(25^{\frac{3}{2}}\)
- \(32^{\frac{3}{5}}\)
- Jibu
-
- 100
- 125
- 8
- \(275^{\frac{3}{2}}\)
- \(16^{\frac{5}{4}}\)
- \(32^{\frac{2}{5}}\)
- \(16^{\frac{3}{2}}\)
- \(125^{\frac{5}{3}}\)
- \(64^{\frac{4}{3}}\)
- Jibu
-
- 64
- 3125
- 256
- \(32^{\frac{2}{5}}\)
- \(27^{−\frac{2}{3}}\)
- \(25^{−\frac{3}{2}}\)
- \(64^{\frac{5}{2}}\)
- \(81^{−\frac{3}{2}}\)
- \(27^{−\frac{4}{3}}\)
- Jibu
-
- 32,768
- \(\frac{1}{729}\)
- \(\frac{1}{81}\)
- \(25^{\frac{3}{2}}\)
- \(9^{−\frac{3}{2}}\)
- \((−64)^{\frac{2}{3}}\)
- \(100^{\frac{3}{2}}\)
- \(49^{−\frac{5}{2}}\)
- \((−100)^{\frac{3}{2}}\)
- Jibu
-
- 1000
- \(\frac{1}{16,807}\)
- si idadi halisi
- \(−9^{\frac{3}{2}}\)
- \(−9^{−\frac{3}{2}}\)
- \((−9)^{\frac{3}{2}}\)
- \(−64^{\frac{3}{2}}\)
- \(−64^{−\frac{3}{2}}\)
- \((−64)^{\frac{3}{2}}\)
- Jibu
-
- -512
- \(−\frac{1}{512}\)
- si idadi halisi
- \(−100^{\frac{3}{2}}\)
- \(−100^{−\frac{3}{2}}\)
- \((−100)^{\frac{3}{2}}\)
- \(−49^{\frac{3}{2}}\)
- \(−49^{−\frac{3}{2}}\)
- \((−49)^{\frac{3}{2}}\)
- Jibu
-
- -343
- \(−\frac{1}{343}\)
- si idadi halisi
Tumia Sheria za Watazamaji ili kurahisisha Maneno na Maonyesho ya Mantiki
Katika mazoezi yafuatayo, kurahisisha.
- \(4^{\frac{5}{8}}·4^{\frac{11}{8}}\)
- \(m^{\frac{7}{12}}·m^{\frac{17}{12}}\)
- \(p^{\frac{3}{7}}·p^{\frac{18}{7}}\)
- \(6^{\frac{5}{2}}·6^{\frac{12}{6}}\)
- \(n^{\frac{2}{10}}·n^{\frac{8}{10}}\)
- \(q^{\frac{2}{5}}·q^{\frac{13}{5}}\)
- Jibu
-
- 216
- n
- \(q^3\)
- \(5^{\frac{1}{2}}·5^{\frac{7}{2}}\)
- \(c^{\frac{3}{4}}·c^{\frac{9}{4}}\)
- \(d^{\frac{3}{5}}·d^{\frac{2}{5}}\)
- \(10^{\frac{1}{3}}·10^{\frac{5}{3}}\)
- \(x^{\frac{5}{6}}·x^{\frac{7}{6}}\)
- \(y^{\frac{11}{8}}·y^{\frac{21}{8}}\)
- Jibu
-
- 100
- \(x^2\)
- \(y^4\)
- \((m^6)^{\frac{5}{2}}\)
- \((n^9)^{\frac{4}{3}}\)
- \((p^{12})^{\frac{3}{4}}\)
- \((a^{12})^{\frac{1}{6}}\)
- \((b^{15})^{\frac{3}{5}}\)
- \((c^{11})^{\frac{1}{11}}\)
- Jibu
-
- \(a^2\)
- \(b^9\)
- c
- \((x^{12})^{\frac{2}{3}}\)
- \((y^{20})^{\frac{2}{5}}\)
- \((z^{16})^{\frac{1}{16}}\)
- \((h^6)^{\frac{4}{3}}\)
- \((k^{12})^{\frac{3}{4}}\)
- \((j^{10})^{\frac{7}{5}}\)
- Jibu
-
- \(h^8\)
- \(k^9\)
- \(j^{14}\)
- \(\frac{x^{\frac{7}{2}}}{x^{\frac{5}{2}}}\)
- \(\frac{y^{\frac{5}{2}}}{y^{\frac{1}{2}}}\)
- \(\frac{r^{\frac{4}{5}}}{r^{\frac{9}{5}}}\)
- \(\frac{s^{\frac{11}{5}}}{s^{\frac{6}{5}}}\)
- \(\frac{z^{\frac{7}{3}}}{z^{\frac{1}{3}}}\)
- \(\frac{w^{\frac{2}{7}}}{w^{\frac{9}{7}}}\)
- Jibu
-
- s
- \(z^2\)
- \(\frac{1}{w}\)
- \(\frac{t^{\frac{12}{5}}}{t^{\frac{7}{5}}}\)
- \(\frac{x^{\frac{3}{2}}}{x^{\frac{1}{2}}}\)
- \(\frac{m^{\frac{13}{8}}}{m^{\frac{5}{8}}}\)
- \(\frac{u^{\frac{13}{9}}}{u^{\frac{4}{9}}}\)
- \(\frac{r^{\frac{15}{7}}}{r^{\frac{8}{7}}}\)
- \(\frac{n^{\frac{3}{5}}}{n^{\frac{8}{5}}}\)
- Jibu
-
- u
- r
- \(\frac{1}{n}\)
- \((9p^{\frac{2}{3}})^{\frac{5}{2}}\)
- \((27q^{\frac{3}{2}})^{\frac{4}{3}}\)
- \((81r^{\frac{4}{5}})^{\frac{1}{4}}\)
- \((64s^{\frac{3}{7}})^{\frac{1}{6}}\)
- Jibu
-
- \(3r^{\frac{1}{5}}\)
- \(2s^{\frac{1}{14}}\)
- \((16u^{\frac{1}{3}})^{\frac{3}{4}}\)
- \((100v^{\frac{2}{5}})^{\frac{3}{2}}\)
- \((27m^{\frac{3}{4}})^{\frac{2}{3}}\)
- \((625n^{\frac{8}{3}})^{\frac{3}{4}}\)
- Jibu
-
- \(9m^{\frac{1}{2}}\)
- \(125n^2\)
- \((x^{8}y^{10})^{\frac{1}{2}}\)
- \((a^{9}by ^{12})^{\frac{1}{3}}\)
- \((r^{8}s^{4})^{\frac{1}{4}}\)
- \((u^{15}v^{20})^{\frac{1}{5}}\)
- Jibu
-
- \(r^{2}s\)
- \(u^{3}v^{4}\)
- \((a^{6}b^{16})^{\frac{1}{2}}\)
- \((j^{9}k^{6})^{\frac{2}{3}}\)
- \((r^{16}s^{10})^{\frac{1}{2}}\)
- \((u^{10}v^5)^{\frac{4}{5}}\)
- Jibu
-
- \(r^{8}s^{5}\)
- \(u^{8}v^{4}\)
- \(\frac{r^{\frac{5}{2}}·r^{−\frac{1}{2}}}{r^{−\frac{3}{2}}}\)
- \(\frac{s^{\frac{1}{5}}·s}{s^{−\frac{9}{5}}}\)
- \(\frac{a^{\frac{3}{4}}·a^{−\frac{1}{4}}}{a^{−\frac{10}{4}}}\)
- \(\frac{b^{\frac{2}{3}}·b}{b^{−\frac{7}{3}}}\)
- Jibu
-
- \(a^3\)
- \(b^4\)
- \(\frac{c^{\frac{5}{3}}·c^{−\frac{1}{3}}}{c^{−\frac{2}{3}}}\)
- \(\frac{d^{\frac{3}{5}}·d}{d^{−\frac{2}{5}}}\)
- \(\frac{m^{\frac{7}{4}}·m^{−\frac{5}{4}}}{m^{−\frac{2}{4}}}\)
- \(\frac{n^{\frac{3}{7}}·n}{n^{−\frac{4}{7}}}\)
- Jibu
-
- m
- \(n^2\)
\(4^{\frac{5}{2}}·4^{\frac{1}{2}}\)
\(n^{\frac{2}{6}}·n^{\frac{4}{6}}\)
- Jibu
-
n
\((a^24)^ {\frac{1}{6}}\)
\((b^{10})^{\frac{3}{5}}\)
- Jibu
-
\(b^6\)
\(\frac{w^{\frac{2}{5}}}{w^{\frac{7}{5}}}\)
\(\frac{z^{\frac{2}{3}}}{z^{\frac{8}{3}}}\)
- Jibu
-
\(\frac{1}{z^2}\)
\((27r^{\frac{3}{5}})^{\frac{1}{3}}\)
\((64s^{\frac{3}{5}})^{\frac{1}{6}}\)
- Jibu
-
\(2s^{\frac{1}{10}}\)
\((r^{9}s^{12})^{\frac{1}{3}}\)
\((u^{12}v^{18})^{\frac{1}{6}}\)
- Jibu
-
\(u^{2}v^{3}\)
kila siku Math
Landscaping Joe anataka kuwa na mraba bustani njama katika mashamba yake. Ana mbolea ya kutosha kufunika eneo la futi za mraba 144. \(144^{\frac{1}{2}}\)Kurahisisha kupata urefu wa kila upande wa bustani yake.
Landscaping Elliott anataka kufanya patio mraba katika yadi yake. Ana saruji ya kutosha kusafisha eneo la futi za mraba 242. \(242^{\frac{1}{2}}\)Kurahisisha kupata urefu wa kila upande wa patio.Round kwa karibu kumi ya mguu.
- Jibu
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Futi 15.6
Gravity Wakati kuweka up mapambo likizo, Bob imeshuka mapambo kutoka juu ya mti yaani 12 miguu mrefu. \(\frac{12^{\frac{1}{2}}}{16^{\frac{1}{2}}}\)Kurahisisha kupata sekunde ngapi zilizochukua kwa ajili ya mapambo kufikia ardhi. Pande zote hadi kumi ya karibu ya pili.
Gravity Ndege imeshuka flare kutoka kimo cha futi 1024 juu ya ziwa. \(\frac{1024^{\frac{1}{2}}}{16^{\frac{1}{2}}}\)Kurahisisha kupata sekunde ngapi ilichukua kwa flare kufikia maji.
- Jibu
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Sekunde 8
Mazoezi ya kuandika
Onyesha mbinu mbili tofauti za algebraic ili kurahisisha\(4^{\frac{3}{2}}\). Eleza hatua zako zote.
Eleza kwa nini usemi\((−16)^{\frac{3}{2}}\) hauwezi kutathminiwa.