"Division of powers with the same base" PPT

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"Division of powers with the same base" PPT

Part I: Preparation for school

Usually the intensity of a person's voice when speaking is 105.

The intensity of the sound made by a motorcycle when it is running is 1011.

How much louder is the sound produced by a motorcycle than when a person is speaking?

Solution: 1011÷105

Division of powers with the same base PPT, part 2: Problem summary

Summarize

Properties of division operations for powers with the same base

When powers with the same base are divided, the base is ____ and the exponent is _____.

Symbol representation: am ÷an =_____

(a≠0, m, n are positive integers, and m>n).

Solve the problem

Usually the intensity of a person's voice when speaking is 105.

The intensity of the sound made by a motorcycle when it is running is 1011.

How much louder is the sound intensity of a motorcycle than a person speaking?

Solution: 1011÷105=1011-5=106

Answer: The sound intensity of a motorcycle is 106 times the sound intensity of a person speaking.

Division of powers with the same base PPT, part three: explanation of examples

Example 1 Calculate the following problems:

⑴ a6÷a2;

⑵ (-b)8÷(-b);

⑶ (ab)4÷(ab)2;

⑷ t2m+3÷t2 (m is a positive integer).

Example 2 Calculate the following problems:

⑴ (-a)3÷a2;

⑵ (x-y)3÷(y-x);

be careful

1. Pay attention to the order of operations

2. Pay attention to the signs (especially the negative sign)

3. Pay attention to the correct use of the properties of each operation

4. Pay attention to the reverse use of various operation properties

5. Pay attention to whether the calculation result is completed

Division of powers with the same base PPT, Part 4: Test and practice

1. Fill in the blanks:

(1) a6÷( ) = a

(2)( )÷x3=x4

(3)ｘ3m÷xm = ( )

(4)x6÷x( )=x3·x

(5) a2n+1÷ a( )=an+1

2. Calculate:

⑵ (-a)5÷(-a);

⑶ (-xy)5÷(-xy)2;

⑷a10n÷a2n (n is a positive integer).

Division of powers with the same base PPT, Part 5: Summary

⒈ Operational properties of division of powers with the same base;

2. What should you pay attention to when applying the operation properties of power division with the same base?

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"Division of Powers with the Same Base" PPT download:

"Division of powers with the same base" PPT download Part 1 content: Knowledge review 1. Division of powers with the same base, base ____, exponent ___. 2. aman=____ (a0, m, n are all positive integers, and mn) 3 .Calculation: (1) 279973 (2) b2mbm-1 (m is an integer greater than 1)..

"Division of powers with the same base" PPT courseware 2:

"Division of Powers with the Same Base" PPT Courseware 2 Learning Objectives 1. Through the operational properties of multiplication of powers with the same base, derive the operational properties of division of powers with the same base. 2. Be able to use the operational properties of division of powers with the same base to perform calculations. 3. Be able to utilize the operational properties of exponents with the same base..

"Division of Powers with the Same Base" PPT courseware:

"Division of powers with the same base" PPT courseware review old knowledge and learn new things 1. The operation rule of multiplication of powers with the same base is aman=am+n (m and n are positive integers) 2. The operation rule of power exponentiation is (am)n=amn( m, n are positive integers) 3. The operation rule for the power of the product is (ab)n=anbn (n is..

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Update Time: 2024-09-05

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