1.6 评价涉及强权的数值和变量表达方式
Section outline
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Casey missed three days of school this week because of a nasty cold. When he returned to school on Thursday he asked his math teacher what he had missed. Miss Brown wrote a problem on a sheet of paper and handed it to Casey. When he arrived home from school Casey looked at his homework which was the following problem:
::凯西因为感冒而错过了本周的三天学校。当他星期四回到学校时,他问数学老师他错过了什么。布朗小姐在一张纸上写了一个问题,并把它交给凯西。当他从学校回家的时候,凯西看了他的作业,这是下面的问题:Casey didn’t know what to do with . How can he rewrite the problem so that he understands what operations to perform?
and
::凯西不知道与54和(-2)4有什么关系。 他如何重写问题,以便他了解要执行什么行动?In this concept, you will learn how to evaluate numerical expressions involving powers.
::在此概念中,您将学会如何评价涉及权力的数字表达式。Evaluating Expressions Involving Powers
::评价涉及权力方的表达方式A numerical expression is an expression made up only of numbers and operations but an expression written with a variable in it, is called a variable expression .
::数字表达式是一个仅由数字和操作组成的表达式,但其中写有变量的表达式则称为变量表达式。Both a numerical expression and a variable expression can include powers.
::数字表达式和变量表达式都可以包括权力。A power is the result of multiplying a number by itself one or more times. The number 16 is the fourth power of 2.
::一个功率是数字本身乘以一个或多个倍的结果。数字 16 是 2 的第四功率 。. The number raised to the power is called the base and the number expressing the power is called the exponent . The exponent tells you how many times to multiply the base times itself.
. The ‘fourth power of 2’ or ‘2 to the power of 4’ can be written as
::2x2x2xx2=16。 ` 2 或 ' 2 到 4 ' 的第四功率可以写为 24. 向该功率提出的数字称为基数,表示该功率的号码称为推算数。 推算数告诉你乘基数本身多少倍。 63= 6x6x6x6 。Let’s look at an example.
::让我们举个例子。Evaluate the following expression:
::评价以下表述:First, expand the powers to see the operations you need to perform.
::首先,扩大权力范围,看您需要执行的操作。
::63=6x6x6 和 52=5x5 next, 以扩展格式写入表达式 。Next, apply the order to operations (PEMDAS) to evaluate the expanded expression.
::下一步,对操作( PEMDAS) 应用此命令来评价扩展表达式 。Then, in order from left to right, multiply: and write the new expression.
::然后,按照从左到右的顺序,乘以:6x6=36x6=216,并写下新的表达式。Then, multiply: and write the new expression.
::然后,乘以: 5x5=25 然后写新表达式 。Next, from left to right, add: and write the new expression.
::下, 从左到右, 添加: 216+25=241, 并写入新表达式 。Then, add:
::然后加上:241+25=266The answer is 266.
::答案是266Let’s look at another example.
::让我们再看看另一个例子。First, expand the powers to see the operations you need to perform.
::首先,扩大权力范围,看您需要执行的操作。
::62=6x6和33=3x3x3x3Next, write the expression in expanded form.
::下一步,用扩展格式写出表达式。Next, apply the order to operations (PEMDAS) to evaluate the expanded expression.
::下一步,对操作( PEMDAS) 应用此命令来评价扩展表达式 。Then, in order from left to right multiply: and write the new expression.
::然后,按照从左到右的顺序乘以: 6x6=36, 并写下新的表达式 。Then, multiply: and write the new expression.
::然后,乘以:3x3x3x3=27, 并写下新表达式 。Next, from left to right, add: and write the new expression.
::接下来,从左到右,加上:36+15=51,并写下新表达式。Then, add:
and write the new expression.
::然后,加上:51+27-78 并写下新表达式。Next, subtract:
::下一步,减去:78-11=67The answer is 67.
::答案是67。Examples
::实例Example 1
::例1Earlier, you were given a problem about Casey and his confusing homework.
::早些时候,你得到一个问题 凯西和他令人困惑的作业。Casey needs to expand the powers so he can see what operations he has to do to evaluate the expression.
::凯西需要扩大权力范围 这样他才能看清 他必须做什么行动来评价表达方式First, evaluate the two powers given in the problem.
::首先,评估这一问题中赋予的两项权力。
::54=5x5x5x5=625和(-2)42222×2=16Next, replace the powers in the expression with their values.
::接下来,将表达式中的权力替换为它们的值。
::625+16+12 然后,添加。The answer is 653.
::答案是653Example 2
::例2Evaluate the following variable expression when .
::评估以下变量表达式时x=4 。
::2x3-12First, substitute the value into the expression.
::首先,将值 x=4 替换为表达式。Next, expand the power.
::下一个,扩展电源。
:4)3=( 4x4x4) 下一步, 以扩展格式写入表达式 。
Then, perform the operation in the parenthesis.
::然后在括号里做手术Multiply: and write the new expression.
::乘以: 4x4=16x4=64, 并写入新表达式 。Next, multiply: and write the new expression.
::下一步,乘以:2(64)=128,并写下新表达式。Then, subtract.
::然后,减。The answer is 116.
::答案是116Example 3
::例3Evaluate the following numerical expression.
::评估以下数字表达式。First, expand the powers.
::首先,扩大权力。
::2x2x2x2和3x3x3x3Next, write the expression in expanded form.
::下一步,用扩展格式写出表达式。Then, in order from left to right multiply: and write the new expression.
::然后,按照从左到右的顺序乘以: 2x2xx2xx2xx2=16, 并写下新的表达式 。Next, multiply: and write the new expression.
::下一个, 乘以: 3x3x3=27, 并写入新表达式 。Then, in order from left to write, subtract: and write the new expression.
::然后,按照左边的顺序写,减去:20-16=4,并写下新的表达式。Next, add: and write the new expression.
::下加: 4+1=5, 并写下新表达式 。Then add:
::然后加上:5+27=32The answer is 32.
::答案是32个Example 4
::例4Evaluate the following variable expression when and .
::当 m=3andn=2 时, 评估以下变量表达式 。
::n5+3m2-15First, substitute and into the variable expression.
::首先,将 m=3andn=2 替换为变量表达式。
::25+3(3)2- 15 next, 扩展权力范围: 25=( 2x2x2x2x2x2) 和 (3)2=( 3x3)Then, write the expression in expanded form.
::然后,用扩展的形式写出表达式。Then, perform the operation in the parenthesis.
::然后在括号里做手术First, multiply: and write the new expression.
::首先,乘以( 3x3) =( 9) 并写入新表达式 。Next, multiply: to clear the parenthesis. Write the new expression.
::下一个, 乘以 3( 9) = 27 来清除括号。 写入新表达式 。Next, multiply: Write the new expression.
::下一个, 乘以: 2x2=4x2=8x2=8x2=16x2=32 写下新表达式 。Next, add: and write the new expression.
::下加: 32+27=59 并写下新表达式 。
::59- 15 然后, 减去: 59- 15= 44The answer is 44.
::答案是44Review
::回顾Expand and evaluate each power.
::扩大并评估每个力量。1.
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Evaluate each numerical expression. Remember to apply PEMDAS to evaluate the expression accurately.
::评估每个数字表达式。 记住应用 PEMDAS 来准确评价表达式 。9.
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Evaluate each variable expression using the given values.
::使用给定值评价每个变量表达式。16. , when
::16.a+42-2,a=3时17.
::a3+14, 当 a=6时。18.
::18. A=4时2a2-1619.
::19. 5b3+12, b=-220.
::20. 2x2+52,x=4Review (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
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