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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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.