1.8用幂来表示重复值的乘积

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• 选择节用幂来表示重复值的乘积

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  用幂来表示重复值的乘积

  

  [Figure 1]

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  Cherry is training to be an interior designer. One of her projects is to make notes on every room in which she spends time. Cherry soon gets sick of writing down all the dimensions: 18 feet wide x 18 feet long x 18 feet high. Is there an easier way for Cherry to note down all the same information?
  ::樱桃是一个内部设计师的训练。 她的项目之一是在她花时间的每个房间做笔记。 樱桃很快会厌倦写下所有尺寸: 18英尺宽 x 18英尺长 x 18英尺宽 x 18英尺高。 樱桃是否有一个更容易的办法来记录所有相同的信息?

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  In this concept, you will learn how to write the product of repeated values using powers.
  ::在这个概念中,你将学会如何用力量来写出反复价值的产物。

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  Exponents
  ::指数

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  Factors  are a sequence of numbers that are multiplied by each other, like  $\begin{array}{r}2\times 3\times 4\end{array}$ , where 2, 3, and 4 are factors, or  $\begin{array}{r}5\times 5\times 5\times 5\end{array}$ , where 5, 5, 5, and 5 are factors.
  ::系数是数字的顺序,相互乘以,例如2×3×4,其中2×3×4为因数,2×3×4为因数,或5×5×5×5×5×5,其中5×5为因数。

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  Repeated factors can be rewritten as a power using an  exponent.  Remember, the  exponent  is the little number that tells you how many times to multiply the base by itself.
  ::重复因数可以使用指数重写为动力。 提醒要记住, 提示是小数数, 表示有多少次自己乘以基数 。

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  Consider this expression:
  ::考虑这一表述:

  $$\begin{array}{r}7\times 7\times 7=\underset{\_}{}\end{array}$$

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  There are three 7’s being multiplied. Since 7 is the number being multiplied, the base is 7. Since the 7 is multiplied by itself 3 times, the exponent (also called the power) is 3. 
  ::乘以三七乘以七乘以七乘以七乘以七乘以七乘以七乘以七乘以七乘以三乘以七乘以七乘以三乘以三乘以三,引号(也称为电源)为三乘以三

  $$\begin{array}{r}7\times 7\times 7=7^3\end{array}$$

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  Examples
  ::实例

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  Example 1
  ::例1

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  Earlier, you were given a problem about Cherry and her lengthy dimensions.
  ::早些时候,你得到一个问题 关于樱桃和她长长的尺寸。

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  Cherry wants to know an easier alternative to writing 18 feet wide x 18 feet long x 18 feet high.
  ::樱桃想知道一个更容易的替代 写作18英尺宽x18英尺长x18英尺高。

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  You now know that when the same number, or factor, is being multiplied repeatedly, you can represent that with an exponent.
  ::您现在知道,当同一个数字或系数被多次乘以时,您可以用一个引号来表示。

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  In Cherry’s case, the base number is 18, and she is multiplying it 3 times, so 3 is the exponent. There is also a particular way to express the exponent 3: you can say the number is "cubed". In this case, since the units, feet, are multiplied by themselves three times also, the resulting units are "feet cubed" or "cubic feet".
  ::在樱桃的案例中,基数是18, 基数是3倍, 她乘以3倍, 所以3是指数。 还有一个表达指数的特殊方式: 你可以说数字是“ 孵化的 ” 。 在这种情况下, 单位, 脚, 本身也乘以3倍, 结果的单位是“ 立方体 ” 或“ 立方脚 ” 。

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  The answer is  $\begin{array}{r}(18\text{ feet}{)}^3\end{array}$ .
  ::答案是(18英尺)3。

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  Cherry can now make her notations much faster by writing 18 ³  ft ³ , or 18 cubed, cubic feet.
  ::樱桃现在可以写183平方英尺 或18立方英尺立方英尺

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  Example 2
  ::例2

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  Write the following as a base with an exponent.
  ::以标语为基准写下以下文字 。

  $$\begin{array}{r}4\times 4\times 4\times 4\end{array}$$

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  First, look at what number is being multiplied by itself, in this case, 4. That number is the base.
  ::首先,看看数字本身是乘以多少,在本案中,是乘以4。 这个数字是基数。

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  Next, write the base, 4, as a full-size number.
  ::下一个,写基数,4,作为一个全尺寸数字。

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  Then, write the power (also 4 in this case, since the base is repeated 4 times), as a small number above and to the right of the base.
  ::然后写下权力(此处还有4个, 因为基数重复4次), 写成比基数上少的数, 并写上基数右侧的数 。

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  The answer is  $\begin{array}{r}{4}^4\end{array}$ .
  ::答案是4 4。

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  Example 3
  ::例3

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  Write the following as a base with an exponent.
  ::以标语为基准写下以下文字 。

  $$\begin{array}{r}6\times 6\times 6\times 6\end{array}$$

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  First, look at what number is being multiplied by itself. In this case, 6. This is the base.
  ::首先,看看数字本身是乘以多少。在这种情况下,是6,这是基数。

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  Next, write the base, 6, as a full-size number.
  ::下一个,写基数,6,作为一个全尺寸数字。

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  Then, write the power, 4 in this case, as a small number above and to the right of the base.
  ::然后,写下权力, 4,在本案中,4, 作为小数的上方, 和基地的右侧。

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  The answer is  $\begin{array}{r}{6}^4\end{array}$ .
  ::答案是6 4。

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  Example 4
  ::例4

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  Write the following as a base with an exponent.
  ::以标语为基准写下以下文字 。

  $$\begin{array}{r}2\times 2\times 2\times 2\times 2\times 2\times 2\end{array}$$

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  First, look at what number is being multiplied by itself. In this case, 2. That means 2 is the base.
  ::首先,看看数字本身是乘以多少。在这种情况下,是2,这意味着基数是2。

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  Next, write the base, 2, as a full-size number.
  ::接下来,写下基数, 2, 一个全尺寸数字 。

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  Then, write the power, 7 in this case, as a small number above and to the right of the base.
  ::然后,写下权力,7,这个情况下,7, 作为一小撮数的上方, 和基地的右侧。

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  The solution is  $\begin{array}{r}{2}^7\end{array}$ .
  ::解决办法是2 7。

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  Example 5
  ::例5

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  Write the following as a base with an exponent.
  ::以标语为基准写下以下文字 。

  $$\begin{array}{r}3\times 3\end{array}$$

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  First, look at what number is being multiplied by itself. In this case, 3. This is the base.
  ::首先,看看数字本身是乘以多少。在这种情况下,是3,这是基数。

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  Next, write the base, 3, as a full-size number.
  ::下一个,写基数,3,全尺寸数字。

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  Then, write the power, 2 in this case, as a small number above and to the right of the base.
  ::然后,写下权力,在这个情况下写上2个,作为上方的一小撮数, 并写到基地的右侧。

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  The answer is  $\begin{array}{r}{3}^2\end{array}$ .
  ::答案是3 2

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  Review
  ::回顾

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  Write each repeated factor using an exponent.
  ::使用引言撰写每个重复因数 。

  1. $\begin{array}{r}4\times 4\times 4\end{array}$
  2. $\begin{array}{r}3\times 3\times 3\times 3\end{array}$
  3. $\begin{array}{r}2\times 2\end{array}$
  4. $\begin{array}{r}9\times 9\times 9\times 9\times 9\end{array}$
  5. $\begin{array}{r}10\times 10\times 10\times 10\times 10\times 10\times 10\end{array}$  
  6.   $\begin{array}{r}1\times 1\times 1\times 1\times 1\times 1\times 1\times 1\times 1\times 1\end{array}$
  7. $\begin{array}{r}3\times 3\times 3\times 3\times 3\times 3\end{array}$
  8. $\begin{array}{r}4\times 4\end{array}$
  9. $\begin{array}{r}7\times 7\times 7\end{array}$
  10. $\begin{array}{r}6\times 6\times 6\times 6\end{array}$
  11. $\begin{array}{r}11\times 11\times 11\end{array}$
  12. $\begin{array}{r}12\times 12\end{array}$
  13. $\begin{array}{r}18\times 18\times 18\end{array}$
  14. $\begin{array}{r}21\times 21\times 21\times 21\end{array}$
  15. $\begin{array}{r}17\times 17\end{array}$

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  Review (Answers) 
  ::回顾(答复)

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  Click   to see the answer key or go to the Table of Contents and click on the Answer Key under the 'Other Versions' option.
  ::单击可查看答题键, 或转到目录中, 单击“ 其他版本” 选项下的答题键 。

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  Resources
  ::资源