We are given a table of vocabulary words.
| Vocabulary Word
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| 1. cube root
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| 2. irrational number
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| 3. Product of Powers Property
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| 4. perfect cube
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| 5. perfect square
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| 6. Power of Powers Property
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| 7. Powers of Products Property
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| 8. scientific notation
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| 9. square root
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We are also given a table of definitions. Let's assign a letter to each definition.
| Definition
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| A. a number that cannot be written in the form ab, where a and b are integers and b ≠0
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| B. a way to express a number as the product of two factors, one greater than or equal to 1 and less than 10, and the other a power of 10
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| C. a number that when multiplied by itself equals the original number
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| D. the cube of an integer
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| E. a number whose cube equals the original number
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| F. To multiply two powers with the same base, keep the common base and add the exponents.
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| G. To multiply two powers with the same exponent and different bases, multiply the bases and keep the exponent.
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| H. a number that is the square of an integer
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| I. When you have an exponent raised to a power, keep the base and multiply the exponents.
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Let's connect each vocabulary word with its definition. We will consider each word one at a time.
1. cube root
The of a number is a number whose cube is equal to that number. For example, the cube root of 8 is equal to 2.
sqrt(8) = sqrt(2 * 2 * 2) = 2
This corresponds to definition E.
| Vocabulary Word
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Definition
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| 1. cube root
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E. a number whose cube equals the original number
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2. irrational number
Numbers that are not are called . An irrational number is a number that cannot be written in the form ab, where a and b are and b ≠0. Let's take a look at a few examples of irrational numbers.
sqrt(3), 5.39275832229..., π
We can see that this corresponds to definition A.
| Vocabulary Word
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Definition
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| 2. irrational number
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A. a number that cannot be written in the form ab, where a and b are integers and b ≠0
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3. Product of Powers Property
Let's consider the of two 3^2 and 3^3.
3^2 * 3^3
The number 3 is first raised to the second power and then to the third power. This means that 3 is multiplied two times and then three times.
3^2 * 3^3 = (3 * 3) * (3 * 3 * 3)
After expanding the powers, we can see that 3 is multiplied five times.
3^2 * 3^3 = (3 * 3) * (3 * 3 * 3) = 3^5
The states that when multiplying two powers with the same base, we add the . This corresponds to definition F.
| Vocabulary Word
|
Definition
|
| 3. Product of Powers Property
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F. To multiply two powers with the same base, keep the common base and add the exponents.
|
4. perfect cube
Recall that the cube root of a number is a number whose cube is equal to that number. For example, the cube root of 27 is 3.
sqrt(27) = sqrt(3 * 3 * 3) = 3
A is a number that is a cube of an integer. Therefore, 27 is a perfect cube. Other examples of perfect cubes are 8, 64, and 125.
&2 * 2 * 2 = 8
&4 * 4 * 4 = 64
&5 * 5 * 5 = 125
We can see that this corresponds to definition D.
| Vocabulary Word
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Definition
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| 4. perfect cube
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D. the cube of an integer
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5. perfect square
We already know that a perfect cube is a number that is a cube of an integer. The definition of a is similar. It is a number that is a square of an integer. A few examples of perfect squares are 4, 9, 16, and 25.
&2 * 2 = 4
& 3 * 3 = 9
&4 * 4 = 16
&5 * 5 = 25
We can see that it corresponds to definition H.
| Vocabulary Word
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Definition
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| 5. perfect square
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H. a number that is the square of an integer
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6. Power of Powers Property
Let's raise 2^3 to the second power.
(2^3)^2
This means that we want to multiply 2^3 by 2^3.
(2^3)^2 = 2^3 * 2^3
Note that by the Product of Powers Property, we can keep the base and add the exponents.
(2^3)^2 = 2^3 * 2^3 = 2^6
The states that to find the power of a power, we multiply the exponents. This corresponds to definition I.
| Vocabulary Word
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Definition
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| 6. Power of Powers Property
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I. When you have an exponent raised to a power, keep the base and multiply the exponents.
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7. Powers of Products Property
Let's multiply two 4^3 and 2^3. We will also expand the powers.
4^3 * 2^3 = 4 * 4 * 4 * 2 * 2 * 2
Now we can use the .
4^3 * 2^3 &= 4 * 4 * 4 * 2 * 2 * 2
&= (4 * 2) * (4 * 2) * (4 * 2) = (4* 2)^3
The states that when multiplying two exponential expressions with the same exponent and different bases, we multiply the bases and keep the exponent the same. This corresponds to definition G.
| Vocabulary Word
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Definition
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| 7. Powers of Products Property
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G. To multiply two powers with the same exponent and different bases, multiply the bases and keep the exponent.
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8. scientific notation
is a way to write very large or very small numbers. Scientists use scientific notation as a more efficient and convenient way of writing such numbers.
83 000 000 = 8.3 * 10^7
0.0000456 = 4.56 * 10^(-5)
The definition of scientific notation is B.
| Vocabulary Word
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Definition
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| 8. scientific notation
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B. a way to express a number as the product of two factors, one greater than or equal to 1 and less than 10, and the other a power of 10
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9. square root
The of a number is a number whose square is equal to that number. For example, the square root of 16 is equal to 4.
sqrt(16) = 4
This corresponds to definition C.
| Vocabulary Word
|
Definition
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| 9. square root
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C. a number that when multiplied by itself equals the original number
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