Section: 整数指数 | 1.7整数指数

Section outline

Horatio is a carpenter building a habitat for tigers at his local zoo. He has been told that the tiger’s enclosure needs to be at least 1720 cubic feet. Horatio has only ever built two animal habitats before, and he was hoping to use one of those as a model. One habitat was $\begin{aligned} 9^{3} \end{aligned}$ cubic feet, and the other was $\begin{aligned} 12^{3} \end{aligned}$ cubic feet. Which of Horatio’s previous habitat designs meets the requirements for the tiger habitat?
::霍拉西奥是一个木匠,他在当地动物园中建造了老虎栖息地。他被告知老虎的围地至少需要1720立方英尺。霍拉西奥以前只建过两个动物栖息地,他希望能用其中的一个作为模型。一个栖息地是93立方英尺,另一个栖息地是123立方英尺。霍拉蒂奥以前的栖息地设计符合老虎栖息地的要求吗?

In this concept, you will learn how powers, bases, and work together.
::在这个概念中,你们将学会如何掌握权力、基础和共同努力。

Whole Number Exponents
::整数指数

An exponent is a little number that shows how many times to multiply a certain number by itself.
::引言是一个小数字,它显示一个数字本身乘以多少倍。

Let's look at an example: $\begin{aligned} 4^{2} \end{aligned}$
::让我们举一个例子:4 2

The large number, 4, is called the base .
::4号大号叫基地

The small number, 2, is called the exponent . This number tells you how many times to multiply the base by itself.
::数字小, 2, 称为指数。这个数字可以告诉你多少次自己乘以基数。

When a base has an exponent of 2, such as $\begin{aligned} 4^{2} \end{aligned}$ , you read it as "four squared".
::当一个基地有2的指数时, 比如4 2, 你把它读成“ 四平方” 。

When a base has an exponent of 3, such as $\begin{aligned} 6^{3} \end{aligned}$ , you read it as "six cubed".
::当一个基点有3的指数时, 比如6 3, 你把它读成“ 6 立方体 ” 。

For all other exponents, you read the exponent as a power . For example,
::对于所有其他的表率,你把表率当作一种力量来读。例如,

$\begin{aligned} 3^{5} \end{aligned}$ is read as "three to the fifth power".
::5是"三对五"

$\begin{aligned} 2^{7} \end{aligned}$ is read as "two to the seventh power".
::2 7 读为“二到七等强”。

$\begin{aligned} 5^{9} \end{aligned}$ is read as "five to the ninth power".
::5 改为“五到九强”。

An exponent tells you how many times the base should be multiplied by itself. If you look at a number with an exponent written out the long way, you can see why exponents are useful.
::expent 告诉您基数应该自行乘以多少倍。如果您看到一个数字, 并用长长的缩略语书写出一个数字, 您可以看到为什么引文有用。

$\begin{aligned} 7 \times 7 \times 7 = 7^{3} \end{aligned}$

In this case, there are three factors of 7. Remember that factors are numbers or variables multiplied by each other.
::在这种情况下,有三个因素,即7。请记住,因素是数字或变量,乘以数字或变量。

$\begin{aligned} 5 \times 5 \times 5 \times 5 \times 5 \times 5 \times 5 \times 5 \times 5 \times 5 = 5^{10} \end{aligned}$

In this case, there are ten factors of 5.
::在这种情况下,有10个因素是5。

Exponents are a multiplication shortcut a lot like the way that multiplication is an addition shortcut.
::指数是一个乘法快捷键, 与乘法是附加快捷键的方式非常相似。

Examples
::实例

Example 1
::例1

Earlier, you were given a problem about Horatio and his tiger housing project.
::先前,你曾遇到Horatio和他的老虎住房项目的问题。

Horatio needs to figure out which dimensions are closest to 1720 cubic feet: 9 ³ cubic feet or 12 ³ cubic feet.
::Horatio需要弄清楚哪些尺寸最接近1720立方英尺:93立方英尺或123立方英尺。

First, write out the factors for each expression.
::首先,写出每个表达式的因数。

$\begin{aligned} 9^{3} = 9 \times 9 \times 9 \end{aligned}$

$\begin{aligned} 12^{3} = 12 \times 12 \times 12 \end{aligned}$

Next, multiply.
::下一个,乘数。

$\begin{aligned} 9 \times 9 & = 81 \times 9 = 729 \\ 12 \times 12 & = 144 \times 12 = 1728 \end{aligned}$

The answer is 12 ³ .
::答案是123号

Horatio can use his old 12 ³ cubic feet habitat design, which even gives the tigers a little extra room.
::Horatio可以使用他的旧123立方英尺的栖息地设计, 甚至给老虎多一点空间。

Example 2
::例2

Write out the factors of $\begin{aligned} 3^{5} \end{aligned}$ , then evaluate the product.
::写出3 5的因数,然后对产品进行评估。

$\begin{aligned} 3^{5} = 3 \times 3 \times 3 \times 3 \times 3 \end{aligned}$

Once you have written out all the factors, simply multiply from left to right.
::一旦你把所有因素都写好了, 简单的从左到右的乘法。

$\begin{aligned} 3 \times 3 = 9 \times 3 = 27 \times 3 = 81 \times 3 = 243 \end{aligned}$
The answer is 243.

Example 3
::例3

Write $\begin{aligned} 6^{3} \end{aligned}$ out in words.
::6个字写3个字

First, identify the base number, which is the big number that will be multiplied by itself. In this case, the base is 6.
::首先,确定基数,即将自行乘以的较大数字。在这种情况下,基数是6。

Next, consider the power, which is the small number that describes how many times the number will be multiplied. In this case, the power is 3, so the base will be multiplied by itself 3 times.
::接下来, 请考虑电量, 也就是数量小的数数, 说明数字将乘以多少倍。在此情况下, 电量是 3 , 所以基数会自行乘以 3 倍。

The solution is "6 times 6 times 6."
::答案是"6乘以6乘以6乘以6"

Example 4
::例4

Write out the factors of $\begin{aligned} 4^{5} \end{aligned}$
::说明4 5的因数

First, remember that factors are numbers that are multiplied by each other to equal a certain value.
::首先,请记住,各种因素是数字,相互乘以等值。

Next, identify the base number, which is the big number that will be multiplied by itself. In this case, the base is 4.
::下一步, 请标明基数, 即将自行乘以的较大数字。在此情况下, 基数是 4 。

Then consider the power, which is the small number that describes how many times the number will be multiplied. In this case the power is 5, so the base will be multiplied by itself 5 times.
::然后考虑电量, 也就是能说明乘以多少倍数的小数数。在这种情况下, 电量是 5, 所以基数会乘以5 倍。

The solution is $\begin{aligned} 4^{5} = 4 \times 4 \times 4 \times 4 \times 4 \end{aligned}$ .
::溶液是 4 5 = 4 × 4 × 4 × 4 × 4 。

Example 5
::例5

Which is the base number: $\begin{aligned} 9^{10} \end{aligned}$ ?
::基数是9 10?

First, remember that the base is the big number that is multiplied by itself.
::首先,记住,基数是乘以本身的较大数字。

Then, remember that the power is the little number that describes how many times to multiply the base by itself.
::那么,请记住, 力量是小数量描述多少倍乘以基数本身。

The answer is that the base in the expression $\begin{aligned} 9^{10} \end{aligned}$ is 9 and the power is 10.
::答案是,910表达式的基数是9, 权力是10。

Review
::回顾

Write each power out in words.
::将每个电源都用文字写出来

$\begin{aligned} 3^{2} \end{aligned}$

$\begin{aligned} 5^{5} \end{aligned}$

$\begin{aligned} 6^{3} \end{aligned}$

$\begin{aligned} 2^{6} \end{aligned}$

$\begin{aligned} 3^{4} \end{aligned}$

$\begin{aligned} 7^{4} \end{aligned}$

$\begin{aligned} 5^{2} \end{aligned}$

$\begin{aligned} 2^{4} \end{aligned}$

$\begin{aligned} 3^{3} \end{aligned}$

$\begin{aligned} 9^{3} \end{aligned}$

Evaluate each expression (they are the same expressions as in problems 1 - 10).
::评估每种表达方式(它们与问题1-10中的表达方式相同)。

$\begin{aligned} 3^{2} \end{aligned}$

$\begin{aligned} 5^{5} \end{aligned}$

$\begin{aligned} 6^{3} \end{aligned}$

$\begin{aligned} 2^{6} \end{aligned}$

$\begin{aligned} 3^{4} \end{aligned}$

$\begin{aligned} 7^{4} \end{aligned}$

$\begin{aligned} 5^{2} \end{aligned}$

$\begin{aligned} 2^{4} \end{aligned}$

$\begin{aligned} 3^{3} \end{aligned}$

$\begin{aligned} 9^{3} \end{aligned}$

Review (Answers)
::回顾(答复)

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。

Resources
::资源

Section outline

Whole Number Exponents ::整数指数

Examples ::实例

Example 1 ::例1

Example 2 ::例2

Example 3 ::例3

Example 4 ::例4

Example 5 ::例5

Review ::回顾

Review (Answers) ::回顾(答复)

Resources ::资源

Whole Number Exponents
::整数指数

Examples
::实例

Example 1
::例1

Example 2
::例2

Example 3
::例3

Example 4
::例4

Example 5
::例5

Review
::回顾

Review (Answers)
::回顾(答复)

Resources
::资源