6.2E: Mazoezi
- Page ID
- 177818
Mazoezi hufanya kamili
Kurahisisha Maneno na Watazamaji
Katika mazoezi yafuatayo, kurahisisha kila kujieleza na watazamaji.
- \(3^5\)
- \(9^1\)
- \((\frac{1}{3})^2\)
- \((0.2)^4\)
- \(10^4\)
- \(17^1\)
- \((\frac{2}{9})^2\)
- \((0.5)^3\)
- Jibu
-
- 10,000
- 17
- \(\frac{4}{81}\)
- 0.125
- \(2^6\)
- \(14^1\)
- \((\frac{2}{5})^3\)
- \((0.7)^2\)
- \(8^3\)
- \(8^1\)
- \((\frac{3}{4})^3\)
- \((0.4)^3\)
- Jibu
-
- 512
- 8
- \(\frac{27}{64}\)
- 0.064
- \((−6)^4\)
- \(−6^4\)
- \((−2)^6\)
- \(−2^6\)
- Jibu
-
- 64
- -64
- \(−(\frac{1}{4})^4\)
- \((−\frac{1}{4})^4\)
- \(−(\frac{2}{3})^2\)
- \((−\frac{2}{3})^2\)
- Jibu
-
- \(−\frac{4}{9}\)
- \(\frac{4}{9}\)
- \(−0.5^2\)
- \((−0.5)^2\)
- \(−0.1^4\)
- \((−0.1)^4\)
- Jibu
-
- -0.0001
- 0.0001
Kurahisisha Maneno Kutumia Mali ya Bidhaa kwa Watazamaji
Katika mazoezi yafuatayo, kurahisisha kila kujieleza kwa kutumia Bidhaa Mali kwa Exponents.
\(d^3·d^6\)
\(x^4·x^2\)
- Jibu
-
\(x^6\)
\(n^{19}·n^{12}\)
\(q^{27}·q^{15}\)
- Jibu
-
\(q^{42}\)
- \(4^5·4^9\)
- \(8^9·8\)
- \(3^{10}·3^6\)
- \(5·5^{4}\)
- Jibu
-
- \(3^{16}\)
- \(5^5\)
- \(y·y^3\)
- \(z^{25}·z^8\)
- \(w^5·w\)
- \(u^{41}·u^{53}\)
- Jibu
-
- \(w^6\)
- \(u^{94}\)
\(w·w^2·w^3\)
\(y·y^3·y^5\)
- Jibu
-
\(y^9\)
\(a^4·a^3·a^9\)
\(c^5·c^{11}·c^2\)
- Jibu
-
\(c^{18}\)
\(m^x·m^3\)
\(n^y·n^2\)
- Jibu
-
\(n^{y+2}\)
\(y^a·y^b\)
\(x^p·x^q\)
- Jibu
-
\(x^{p+q}\)
Katika mazoezi yafuatayo, kurahisisha kila kujieleza kwa kutumia Power Mali kwa Exponents.
- \((m^4)^2\)
- \( (10^3)^6\)
- \((b^2)^7\)
- \((3^8)^2\)
- Jibu
-
- \(b^{14}\)
- \(3^{16}\)
- \((y^3)^x\)
- \((5^x)^y\)
- \((x^2)^y\)
- \((7^a)^b\)
- Jibu
-
- \(x^{2y}\)
- \(7^{ab}\)
Kurahisisha Maneno Kutumia Bidhaa kwa Mali ya Nguvu
Katika mazoezi yafuatayo, kurahisisha kila kujieleza kwa kutumia Bidhaa kwa Power Mali.
- \((6a)^2\)
- \((3xy)^2\)
- \((5x)^2\)
- \((4ab)^2\)
- Jibu
-
- \(25x^2\)
- \(16a^{2}b^{2}\)
- \((−4m)^3\)
- \((5ab)^3\)
- \((−7n)^3\)
- \((3xyz)^4\)
- Jibu
-
- \(−343n^3\)
- \(81x^{4}y^{4}z^{4}\)
Kurahisisha Maneno kwa kutumia Mali kadhaa
Katika mazoezi yafuatayo, kurahisisha kila kujieleza.
- \((y^2)^4·(y^3)^2\)
- \((10a^{2}b)^3\)
- \((w^4)^3·(w^5)^2\)
- \((2xy^4)^5\)
- Jibu
-
- \(w^{22}\)
- \(32x^{5}y^{20}\)
- \((−2r^{3}s^2)^4\)
- \((m^5)^3·(m^9)^4\)
- \((−10q^{2}p^4)^3\)
- \((n^3)^{10}·(n^5)^2\)
- Jibu
-
- \(−1000q^{6}p^{12}\)
- \(n^{40}\)
- \((3x)^{2}(5x)\)
- \((5t^2)^{3}(3t)^{2}\)
- \((2y)^{3}(6y)\)
- \((10k^4)^{3}(5k^6)^{2}\)
- Jibu
-
- \(48y^4\)
- \(25,000k^{24}\)
- \((5a)^{2}(2a)^3\)
- \((12y^2)^{3}(23y)^2\)
- \((4b)^{2}(3b)^{3}\)
- \((12j^2)^{5}(25j^3)^2\)
- Jibu
-
- \(432b^5\)
- \(1200j^{16}\)
- \((25x^{2}y)^3\)
- \((89xy^4)^2\)
- \((2r^2)^{3}(4r)^2\)
- \((3x^3)^{3}(x^5)^4\)
- Jibu
-
- \(128r^{8}\)
- \(27x^{29}\)
- \((m^{2}n)^{2}(2mn^5)^4\)
- \((3pq^4)^{2}(6p^{6}q)^2\)
Katika mazoezi yafuatayo, kuzidisha monomials.
\((6y^7)(−3y^4)\)
- Jibu
-
\(−18y^{11}\)
\((−10x^5)(−3x^3)\)
\((−8u^6)(−9u)\)
- Jibu
-
\(72u^{7}\)
\((−6c^4)(−12c)\)
\((\frac{1}{5}f^8)(20f^3)\)
- Jibu
-
\(4f^{11}\)
\((\frac{1}{4}d^5)(36d^2)\)
\((4a^{3}b)(9a^{2}b^6)\)
- Jibu
-
\(36a^{5}b^7\)
\((6m^{4}n^3)(7mn^5)\)
\((\dfrac{4}{7}rs^2)(14rs^3)\)
- Jibu
-
\(8r^{2}s^5\)
\((\dfrac{5}{8}x^{3}y)(24x^{5}y)\)
\((\frac{2}{3}x^{2}y)(\frac{3}{4}xy^2)\)
- Jibu
-
\(\frac{1}{2}x^{3}y^3\)
\((\dfrac{3}{5}m^{3}n^2)(\dfrac{5}{9}m^{2}n^3)\)
Mazoezi ya mchanganyiko
Katika mazoezi yafuatayo, kurahisisha kila kujieleza.
\((x^2)^4·(x^3)^2\)
- Jibu
-
\(x^{14}\)
\((y^4)^3·(y^5)^2\)
\((a^2)^6·(a^3)^8\)
- Jibu
-
\(a^{36}\)
\((b^7)^5·(b^2)^6\)
\((2m^6)^3\)
- Jibu
-
\(8m^{18}\)
\((3y^2)^4\)
\((10x^{2}y)^3\)
- Jibu
-
\(1000x^{6}y^3\)
\((2mn^4)^5\)
\((−2a^{3}b^2)^4\)
- Jibu
-
\(16a^{12}b^8\)
\((−10u^{2}v^4)^3\)
\((\frac{2}{3}x^{2}y)^3\)
- Jibu
-
\(\frac{8}{27}x^{6}y^3\)
\((\frac{7}{9}pq^4)^2\)
\((8a^3)^{2}(2a)^4\)
- Jibu
-
\(1024a^{10}\)
\((5r^2)^{3}(3r)^2\)
\((10p^4)^{3}(5p^6)^2\)
- Jibu
-
\(25000p^{24}\)
\((4x^3)^{3}(2x^5)^4\)
\((\frac{1}{2}x^{2}y^3)^{4}(4x^{5}y^3)^2\)
- Jibu
-
\(x^{18}y^{18}\)
\((\frac{1}{3}m^{3}n^2)^{4}(9m^{8}n^3)^2\)
\((3m^{2}n)^{2}(2mn^5)^4\)
- Jibu
-
\(144m^{8}n^{22}\)
\((2pq^4)^{3}(5p^{6}q)^2\)
kila siku Math
Barua pepe Kate barua pepe flyer kwa marafiki zake kumi na kuwaambia mbele yake kwa kumi ya marafiki zao, ambao mbele yake kwa kumi ya marafiki zao, na kadhalika. Idadi ya watu wanaopokea barua pepe kwenye mzunguko wa pili ni\(10^2\), kwenye raundi ya tatu ni\(10^3\), kama inavyoonekana katika jedwali hapa chini. Ni watu wangapi watapokea barua pepe kwenye mzunguko wa sita? Kurahisisha usemi ili kuonyesha idadi ya watu wanaopokea barua pepe.
| Round | Idadi ya Watu |
|---|---|
| 1 | 10 |
| 2 | \(10^2\) |
| 3 | \(10^3\) |
| ... | ... |
| 6 | ? |
- Jibu
-
1,000,000
Mshahara bosi wa Jamali anampa ongezeko la 3% kila mwaka siku ya kuzaliwa kwake. Hii inamaanisha kwamba kila mwaka, mshahara wa Jamali ni mara 1.03 mshahara wake wa mwaka jana. Ikiwa mshahara wake wa awali ulikuwa $35,000, mshahara wake baada ya mwaka 1 ulikuwa $35,000 (1.03), baada ya miaka 2 ilikuwa $\(35,000(1.03)^2\), baada ya miaka 3 ilikuwa $\(35,000(1.03)^3\), kama inavyoonekana katika jedwali hapa chini. Mshahara wa Jamali utakuwa nini baada ya miaka 10? Kurahisisha maneno, kuonyesha mshahara wa Jamali kwa dola.
| Mwaka | Mshahara |
|---|---|
| 1 | $35,000 (1.03) |
| 2 | $\(35,000(1.03)^2\) |
| 3 | $\(35,000(1.03)^3\) |
| ... | ... |
| 10 | ? |
Clearance duka idara ni kusafisha nje bidhaa ili kufanya nafasi ya hesabu mpya. Mpango huo ni kuashiria vitu kwa asilimia 30 kila wiki. Hii ina maana kwamba kila wiki gharama ya bidhaa ni 70% ya gharama ya wiki iliyopita. Ikiwa gharama ya awali ya sofa ilikuwa $1,000, gharama ya wiki ya kwanza itakuwa $1,000 (0.70) na gharama ya kipengee wakati wa wiki ya pili itakuwa $\(1,000(0.70)^2\). Jaza meza iliyoonyeshwa hapa chini. Je, itakuwa gharama gani ya sofa wakati wa wiki ya tano? Kurahisisha kujieleza, kuonyesha gharama kwa dola.
| Wiki | Gharama |
|---|---|
| 1 | $1,000 (0.70) |
| 2 | $\(1,000(0.70)^2\) |
| 3 | |
| 4 | ... |
| 5 | ? |
- Jibu
-
$168.07
Kushuka kwa thamani Mara gari mpya ni inaendeshwa mbali na muuzaji, inaanza kupoteza thamani. Kila mwaka, gari hupoteza 10% ya thamani yake. Hii ina maana kwamba kila mwaka thamani ya gari ni 90% ya thamani ya mwaka uliopita. Ikiwa gari jipya lilinunuliwa kwa $20,000, thamani mwishoni mwa mwaka wa kwanza itakuwa $20,000 (0.90) na thamani ya gari baada ya mwisho wa mwaka wa pili itakuwa $\(20,000(0.90)^2\). Jaza meza iliyoonyeshwa hapa chini. Je, itakuwa thamani gani ya gari mwishoni mwa mwaka wa nane? Kurahisisha kujieleza, kuonyesha thamani kwa dola.
| Mwaka | Gharama |
|---|---|
| 1 | $20,000 (0.90) |
| 2 | $\(20,000(0.90)^2\) |
| 3 | |
| ... | ... |
| 8 | ? |
Mazoezi ya kuandika
Tumia Mali ya Bidhaa kwa Watazamaji kuelezea kwa nini\(x·x=x^2\)
- Jibu
-
Majibu yatatofautiana.
Eleza kwa nini\(−5^3=(−5)^3\), lakini\(−5^4 \ne (−5)^4\).
Jorge anadhani\((\frac{1}{2})^2\) is 1. What is wrong with his reasoning?
- Jibu
-
Majibu yatatofautiana.
Eleza kwa\(x^3·x^5\) nini\(x^8\), na si\(x^{15}\).
Self Check
Baada ya kukamilisha mazoezi, tumia orodha hii ili kutathmini ujuzi wako wa malengo ya sehemu hii.
b Baada ya kuchunguza orodha hii, utafanya nini ili uwe na ujasiri kwa malengo yote?