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Biblioteka

IB0-1A: Indices

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Posljednje ažuriranje about 4 years ago
103 questions
Napomena autora:

Index laws with integer indices.

#1

Simplify the following using the index laws.

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#2

Express in simplest form with a prime number base.

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#3

Remove the brackets.

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#4

Simplify the following expressions using one or more of the index laws.

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#5

Simplify, given your answers in simplest rational form.

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#6

Simplify, giving your answers in simplest rational form.

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#7

Write the following without brackets or negative indices.

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#8

Use the index laws to prove that, for positive real numbers a and b, and integer n, the following equations are true.

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#9
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#10
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Pitanje 1
1.

3^2 \times 3^5

Pitanje 2
2.

x^6 \times x^3

Pitanje 3
3.

x^5 \times x^n

Pitanje 4
4.

t^3 \times t^4 \times t^5

Pitanje 5
5.

\dfrac{7^9}{7^5}

Pitanje 6
6.

\dfrac{x^7}{x^3}

Pitanje 7
7.

\dfrac{t^6}{t^x}

Pitanje 8
8.

t^{3m} \div t

Pitanje 9
9.

\left(5^3\right)^2

Pitanje 10
10.

\left(t^4\right)^3

Pitanje 11
11.

\left(y^3\right)^m

Pitanje 12
12.

\left(a^{3m}\right)^4

Pitanje 13
13.

121

Pitanje 14
14.

32

Pitanje 15
15.

81

Pitanje 16
16.

4^2

Pitanje 17
17.

25^2

Pitanje 18
18.

7^t \times 49

Pitanje 19
19.

3^a \div 9

Pitanje 20
20.

8^p \div 4

Pitanje 21
21.

\dfrac{7^n}{7^{n-2}}

Pitanje 22
22.

\dfrac{9}{3^x}

Pitanje 23
23.

\left(25^t\right)^2

Pitanje 24
24.

16^{k-3} \times 2^{-k}

Pitanje 25
25.

\dfrac{4^a}{2^b}

Pitanje 26
26.

\dfrac{8^x}{16^y}

Pitanje 27
27.

\dfrac{125^{x+1}}{5^{x-1}}

Pitanje 28
28.

\dfrac{27^{a+2}}{3^a \times 9^a}

Pitanje 29
29.

\left(xy\right)^2

Pitanje 30
30.

\left(ab\right)^3

Pitanje 31
31.

\left(xyz\right)^2

Pitanje 32
32.

\left(3b\right)^3

Pitanje 33
33.

\left(5a\right)^4

Pitanje 34
34.

\left(10xy\right)^5

Pitanje 35
35.

\left(\dfrac{p}{q}\right)^2

Pitanje 36
36.

\left(\dfrac{x}{3}\right)^4

Pitanje 37
37.

\left(\dfrac{5}{z}\right)^3

Pitanje 38
38.

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

Pitanje 39
39.

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

Pitanje 40
40.

4b^2 \times 2b^3

Pitanje 41
41.

\dfrac{a^6b^3}{a^4b}

Pitanje 42
42.

3ab^2 \times 2a^3

Pitanje 43
43.

\dfrac{5x^3y^2}{15xy}

Pitanje 44
44.

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

Pitanje 45
45.

\dfrac{24t^6 r^4}{15t^6 r^2}

Pitanje 46
46.

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

Pitanje 47
47.

\dfrac{10k^7}{(2k)^5}

Pitanje 48
48.

3^0

Pitanje 49
49.

6^{-1}

Pitanje 50
50.

4^{-1}

Pitanje 51
51.

5^0

Pitanje 52
52.

4^2

Pitanje 53
53.

4^{-2}

Pitanje 54
54.

5^3

Pitanje 55
55.

5^{-3}

Pitanje 56
56.

7^2

Pitanje 57
57.

7^{-2}

Pitanje 58
58.

10^3

Pitanje 59
59.

10^{-3}

Pitanje 60
60.

\left(\dfrac{1}{2}\right)^0

Pitanje 61
61.

\dfrac{5^4}{5^4}

Pitanje 62
62.

2t^0, for t \neq 0.

Pitanje 63
63.

\left(2t\right)^0, for t \neq 0.

Pitanje 64
64.

7^0

Pitanje 65
65.

3 \times 4^0

Pitanje 66
66.

\dfrac{5^3}{5^5}

Pitanje 67
67.

\dfrac{2^6}{2^{10}}

Pitanje 68
68.

\dfrac{x^4}{x^9}

Pitanje 69
69.

\left(\dfrac{3}{8}\right)^{-1}

Pitanje 70
70.

\left(\dfrac{2}{3}\right)^{-1}

Pitanje 71
71.

\left(\dfrac{1}{5}\right)^{-1}

Pitanje 72
72.

2^{0}+2^{1}

Pitanje 73
73.

5^{0} - 5^{-1}

Pitanje 74
74.

3^{0} + 3^{1} - 3^{-1}

Pitanje 75
75.

\left(\dfrac{1}{3}\right)^{-2}

Pitanje 76
76.

\left(\dfrac{2}{3}\right)^{-3}

Pitanje 77
77.

\left(1\dfrac{1}{2}\right)^{-3}

Pitanje 78
78.

\left(\dfrac{4}{5}\right)^{-2}

Pitanje 79
79.

\left(2\dfrac{1}{2}\right)^{-2}

Pitanje 80
80.

(3b)^{-1}

Pitanje 81
81.

3b^{-1}

Pitanje 82
82.

7a^{-1}

Pitanje 83
83.

(7a)^{-1}

Pitanje 84
84.

\left(\dfrac{1}{t}\right)^{-2}

Pitanje 85
85.

\left(\dfrac{3x}{y}\right)^{-1}

Pitanje 86
86.

(5t)^{-2}

Pitanje 87
87.

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

Pitanje 88
88.

xy^{-1}

Pitanje 89
89.

(xy)^{-1}

Pitanje 90
90.

xy^{-3}

Pitanje 91
91.

(xy)^{-3}

Pitanje 92
92.

(3pq)^{-1}

Pitanje 93
93.

3(pq)^{-1}

Pitanje 94
94.

3pq^{-1}

Pitanje 95
95.

\dfrac{(xy)^3}{y^{-2}}

Pitanje 96
96.

\left(5x^{-2}y^3\right)^3

Pitanje 97
97.

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

Pitanje 98
98.

\left(\dfrac{3r^{-3}}{t}\right)^{-2}

Pitanje 99
99.

\left(\dfrac{2p}{5q^{-2}}\right)^{-3}

Pitanje 100
100.

\dfrac{1}{a^{-n}}=a^n

Pitanje 101
101.

\left(\dfrac{a}{b}\right)^{-n}=\dfrac{b^n}{a^n}

Pitanje 102
102.

Find the smaller of 2^{125} and 3^{75} without a calculator.

Hint: 2^{125} = (2^5)^{25}.

Pitanje 103
103.

Order the following numbers, starting with smallest at the top and largest at the bottom. Do not use a calculator. Show your work to prove how you solved this problem.

  1. 10^24

  2. 5^{36}

  3. 2^{90}

  4. 3^{60}