Interactive multiple-choice quiz: exponents and scientific notation الوحدة الأولى ريفيل
This assessment covers the concept of writing repeated multiplication as powers. Students must identify equivalent expressions for given product sequences.
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اختبار شهادة تدريبي مؤقت للصف والمادة والفصل نفسه.
اختر إجابة واحدة لكل سؤال. عند الاختيار ستظهر النتيجة فورًا: الأخضر صحيح، والأحمر خطأ، وسيظهر تفسير الإجابة مباشرة إن كان متوفرًا. وبعد آخر سؤال ستظهر الدرجة النهائية تلقائيًا.
Which of the following is equivalent to the expression $\frac{2}{3}\cdot\frac{2}{3}\cdot\frac{2}{3}\cdot\frac{2}{3}\cdot(-5)\cdot(-5)\cdot(-5)\cdot(-5)\cdot(-5)$?
Question 2
1
Points: 1
Which of the following is equivalent to the expression $\frac{2}{3}\cdot\frac{2}{3}\cdot\frac{2}{3}\cdot\frac{2}{3}\cdot(-5)\cdot(-5)\cdot(-5)\cdot(-5)\cdot(-5)$?
Explanation
In the given expression, the fraction $\frac{2}{3}$ is multiplied by itself 4 \times, which is represented as $(\frac{2}{3})^4$. The number -5 is multiplied by itself 5 \times, which is represented as (-5)5. Multiplying these results gives $(\frac{2}{3})^4 \cdot (-5)^5$.
Question 3
2
Points: 10
Write the expression a× a× b× a× b× a× a× b× b using exponents.
Question 4
3
Points: 10
Evaluate 83+(-3)3.
Question 5
4
Points: 10
Evaluate a4+b2 if a=-3 and b=6.
Question 6
5
Points: 10
Evaluate x2+(y3-85) if $x=-\frac{1}{3}$ and y=5.
Question 7
6
Points: 10
Interstate 90 stretches almost $2^4\cdot7^2\cdot4$ miles across the United States. Interstate 70 stretches almost $2^3\cdot5^2\cdot11$ miles across the United States. How much longer is Interstate 90 than Interstate 70?
Question 8
7
Points: 10
Write the expression using exponents: $(-7)\cdot(-7)\cdot5\cdot5\cdot5\cdot5$.
Question 9
8
Points: 10
Write the expression using exponents: n× n× p× p× r× r× r.
Question 10
9
Points: 10
Evaluate the numerical expression 34-(-4)2.
Question 11
10
Points: 10
Evaluate the numerical expression 6+26.
Question 12
11
Points: 10
Evaluate x3-y2 if x=2 and $y=\frac{3}{4}$.
Question 13
12
Points: 10
Evaluate (g+h)3 if g=2 and h=-3.
Question 14
13
Points: 10
Replace the box with <, >, or = to make a true statement: $(-3)^4\mathbin{\square}(-4)^3$.
Question 15
14
Points: 10
A scientist estimates that there would be $2^5\cdot3^3\cdot10^5$ bacteria in a Petri dish. How many bacteria is this?
Question 16
15
Points: 10
Simplify the expression $4^5\cdot4^3$.
Question 17
16
Points: 10
Simplify the expression x4× x6.
Question 18
17
Points: 10
Simplify the expression -2a(3a4).
Question 19
18
Points: 10
Simplify $\frac{z^{12}}{z^4}$.
Question 20
19
Points: 10
The table shows the seating capacity of two different facilities. About how many times as great is the capacity of Madison Square Garden in New York City as that of a typical movie theater?
Question 21
20
Points: 10
Simplify the expression $\frac{2^2\cdot3^3\cdot4^5}{2\cdot3\cdot4^4}$.
Question 22
21
Points: 10
Simplify the expression $\frac{24k^9}{6k^5}$.
Question 23
22
Points: 10
Bolivia has a population of 107 people, while Aruba has a population of 105 people. The Philippines has a population that is 103 \times as great as Aruba's population. Which statement is true?
A publisher sells 106 copies of a science fiction book and 103 copies of a mystery book. How many \times as many science fiction books were sold?
Question 31
30
Points: 10
Simplify $\frac{45x^{15}}{9x^{10}}$.
Question 32
31
Points: 10
Simplify the expression (63)5.
Question 33
32
Points: 10
Simplify the expression (x4)7.
Question 34
33
Points: 10
Simplify the expression (7w7)3.
Question 35
34
Points: 10
Simplify the expression (-5w2z8)3.
Question 36
35
Points: 10
The floor of the commons room at King Middle School is a square with side length 3x2y3 feet. Square tiles with side length xy feet will cover the floor. How many tiles will it take?
Question 37
36
Points: 10
Simplify (72)3.
Question 38
37
Points: 10
Simplify (83)3.
Question 39
38
Points: 10
Simplify (d7)6.
Question 40
39
Points: 10
Simplify (z7)3.
Question 41
40
Points: 10
Simplify (2m5)6.
Question 42
41
Points: 10
Simplify (7a5b6)4.
Question 43
42
Points: 10
Simplify (-3w3z8)5.
Question 44
43
Points: 10
Simplify (-5r4s10)4.
Question 45
44
Points: 10
Which is greater: 1{,}000 or (62)3?
Question 46
45
Points: 10
Simplify m0, where $m\ne0$.
Question 47
46
Points: 10
Express a-5 using a positive exponent.
Question 48
47
Points: 10
Express the fraction $\frac{1}{9^7}$ using a negative exponent.
Question 49
48
Points: 10
Simplify $3^9\cdot3^{-4}$.
Question 50
49
Points: 10
Simplify $\frac{b^{-7}}{b^{-4}}$.
Question 51
50
Points: 10
An American green tree frog tadpole is about 0.00001=10-5 kilometer long when it hatches. The largest indoor swimming pool is 10-1 kilometer wide. How many \times longer is the pool's width than the tadpole's length?
Question 52
51
Points: 10
Simplify 460.
Question 53
52
Points: 10
Simplify w0, where $w\ne0$.
Question 54
53
Points: 10
Express 8-4 using a positive exponent.
Question 55
54
Points: 10
Express y-9 using a positive exponent.
Question 56
55
Points: 10
Express the fraction $\frac{1}{d^6}$ using a negative exponent.
Question 57
56
Points: 10
Express the fraction $\frac{1}{10^5}$ using a negative exponent.
Question 58
57
Points: 10
Simplify $9^4\cdot9^{-6}$.
Question 59
58
Points: 10
Simplify y-9× y3.
Question 60
59
Points: 10
Simplify $\frac{x^{-8}}{x^{-12}}$.
Question 61
60
Points: 10
Simplify $\frac{a^{-13}}{a^{-2}}$.
Question 62
61
Points: 10
Simplify $8^{-7}\cdot8^7\cdot10^4\cdot10^{-4}$.
Question 63
62
Points: 10
Write $9.931\times10^5$ in standard form.
Question 64
63
Points: 10
Write $6.02\times10^{-4}$ in standard form.
Question 65
64
Points: 10
A calculator screen shows 2.4E{-3}. Which pair gives two equivalent representations of the number?
Question 66
65
Points: 10
Which expression represents 8{,}785{,}000{,}000 in scientific notation?
Question 67
66
Points: 10
Which expression represents 0.524 in scientific notation?
Question 68
67
Points: 10
A plant cell has a diameter of $1.3\times10^{-8}$ kilometer. Is it more appropriate to report the diameter as $1.3\times10^{-8}$ kilometer or $1.3\times10^{-2}$ millimeter?
Question 69
68
Points: 10
The distance from Earth to the Moon is 238{,}900 miles. Write an estimation in scientific notation for the distance.
Question 70
69
Points: 10
The table shows the approximate attendance and average ticket price for four Major League Baseball teams. Which team had the most revenue from ticket sales?
Question 71
70
Points: 10
Write $1.6\times10^3$ in standard form.
Question 72
71
Points: 10
Write $1.49\times10^{-7}$ in standard form.
Question 73
72
Points: 10
A calculator shows 8.3E{-6}. Write this number in standard form.
Question 74
73
Points: 10
A calculator shows 7E{11}. Write this number in standard form.
Question 75
74
Points: 10
Write 2{,}204{,}000{,}000 in scientific notation.
Question 76
75
Points: 10
Write 0.0000000642 in scientific notation.
Question 77
76
Points: 10
Is it more appropriate to report a 5K race distance as 5 km or $5\times10^6$ mm?
Question 78
77
Points: 10
The population of Florida was 20{,}612{,}439. Which option gives a possible estimation in scientific notation?
Question 79
78
Points: 10
The diameter of a grain of sand is 0.0024 inch. Write it in scientific notation.
Question 80
79
Points: 10
A dime is $1.35\times10^{-3}$ meter thick. What would be the height, in meters, of a stack of 1 million dimes?
Question 81
80
Points: 10
In a recent year, the population of China was about $1.3\times10^9$. The population of the United States was about 308{,}745{,}538. About how many \times as great was China's population as the United States population?
Question 82
81
Points: 10
Which of the following is the sum $(8.41\times10^3)+(9.71\times10^4)$ written in scientific notation?
Question 83
82
Points: 10
In 2005, $8.1\times10^{10}$ text messages were sent in the United States. In 2010, the number had risen to 1{,}810{,}000{,}000{,}000. About how many \times as great was the 2010 number as the 2005 number?
Question 84
83
Points: 10
There are about $3\times10^{11}$ stars in our galaxy and 1011 galaxies. How many stars are in the observable universe?
Question 85
84
Points: 10
A humpback whale weighs 80{,}000 pounds ($8\times10^4$). A krill weighs $2.1875\times10^{-3}$ pound. About how many \times as great is the whale's weight?
Question 86
85
Points: 10
Evaluate $(1.28\times10^5)+(1.13\times10^3)$.
Question 87
86
Points: 10
Evaluate $(7.26\times10^6)-(1.3\times10^4)$.
Question 88
87
Points: 10
The speed of light is $1.86\times10^5$ miles per second. The distance to Sirius is $5.062\times10^{13}$ miles. About how many seconds does it take light to travel from Sirius to Earth?
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