"Integer Exponential Powers" Fraction PPT

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"Integer Exponential Powers" Fraction PPT

Part One: [Learning Objectives]

1. Master the operational properties of integer exponential powers.

2. Perform simple exponentiation operations within a range of integers.

[Learning Key Points]

Master the operation properties of integer exponent powers, especially the operation of negative integer exponent powers.

[Difficulties in learning]

Understand the generation process of negative integer exponential powers and the expansion process of the power arithmetic rule.

Integer exponent power PPT, the second part of the content: knowledge analysis

Knowledge Module 1 Explore the operation rules of negative integer exponential powers

Operational properties of positive integer exponential powers:

(1) Multiplication of powers with the same base: am·an=_______ (m and n are positive integers).

(2) Power of power: (am)n=_______ (m, n are positive integers).

(3) Power of product: (ab)n=_______ (n is a positive integer).

(4) Division of powers with the same base: am÷an=_______(a≠0, m and n are positive integers, m>n).

(5) Power of the fraction: _______=_______ (n is a positive integer).

(6)0 is an exponential power: a0=_______ (a≠0).

think

Can the exponent m in am be a negative integer? If so, what does a negative integer power am represent?

1. Calculation: a3 ÷a5=? (a ≠0)

Knowledge Module 2 Comprehensive Application of Integer Exponential Power Arithmetic Rules

think

Can you now tell what am means when m is a positive integer, 0, and a negative integer respectively?

(1) According to the operation properties of integer exponent powers, when m and n are integers, am ÷an=am-n

That is, division of powers with the same base can be converted into multiplication of powers with the same base.

Integer exponent power PPT, the third part: summary

Operational properties of integer exponent powers

(1)am·an=am+n (m and n are integers);

(2)(am)n=amn (m, n are integers);

(3)(ab)n=anbn (n is an integer).

Integer exponent powers PPT, part 4 content: scientific notation

Remember:

Scientific notation: Numbers with an absolute value greater than 10 are recorded in the form a×10n, where 1≤a<10 and n is a positive integer.

For example, 864000 can be written as _____.

Thinking: How to express 0.0000864 in scientific notation?

How to express some numbers with large absolute values ​​using scientific notation:

That is, using the positive integer power of 10, a number with an absolute value greater than 10 is expressed in the form of a×10n, where n is a positive integer, 1 ≤ �a �<10. n is equal to the number of digits in the original number minus 1.

How to express some numbers whose absolute value is less than 1 using scientific notation:

That is, using the negative integer power of 10, a number with an absolute value less than 1 is expressed in the form of a×10-n, where n is a positive integer, 1 ≤ �a �<10. n is equal to the first non-zero digit of the original number The number of all leading zeros (special note: including the zero before the decimal point).

Integer exponent powers PPT, part 5 content: Class summary

Integer exponent

1. Zero exponent power: when a≠0, a0=1.

2. Negative integer exponent power: when n is a positive integer, a-n =

Operational properties of integer exponential powers:

(1) am·an=am+n (m, n is an integer, a≠0)

(2) (ab) m=ambm (m is an integer, a≠0, b≠0)

(3) (am)n=amn (m, n is an integer, a≠0)

Use scientific notation to represent a number with an absolute value less than 1

A number with an absolute value less than 1 is expressed in the form of a×10-n in scientific notation, 1≤│a│<10, n is the number of all 0s (including the decimal point) before the first number that is not 0 in the original number The previous one is 0).

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For more information about the "Fractional Integer Exponential Powers" PPT courseware, please click the Fractional PPT Integer Exponential Powers PPT tag.

"Integer Exponential Powers" Fraction PPT teaching courseware:

"Integer Exponent Powers" Fractional PPT Teaching Courseware Part One Content: Learning Objectives 1. Understand and master the operational properties of negative integer exponent powers. (Key Points) 2. Understand the properties of integer exponent powers and apply them to solve practical problems. (Difficulty) Review old knowledge and talk about it...

"Integer Exponential Powers" Fraction PPT download:

"Integer Exponential Powers" Fractional PPT Download Part One: Knowledge Review What are the operational properties of positive integer exponent powers? Thinking: Some larger numbers are suitable to be expressed in scientific notation. The speed of light is about meters/second. The radius of the sun is about kilometers. The world population in 2010 is about you..

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Update Time: 2024-11-08

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