"Division of Powers with the Same Base" Operation of Integers PPT Courseware 3

Description

"Division of Powers with the Same Base" Operation of Integers PPT Courseware 3

Review and consolidate

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

That is: multiply powers with the same base, keep the base unchanged, and add the exponents.

2. Power of power: (am) n=amn (m and n are both positive integers)

That is: raising powers, the base remains unchanged, and the exponents are multiplied.

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

That is: the power of the product is equal to the product of the respective powers of the factors in the product.

Division rules for powers with the same base:

When powers with the same base are divided, the base remains unchanged and the exponents are subtracted.

That is, am÷an=am-n(a≠0, m and n are both positive integers, m>n)

Notice:

Conditions: ① Division ② Powers with the same base

Result: ①The base remains unchanged ②The exponents are subtracted

example

Example 1 Calculation:

(1)x8÷x2; (2) a4÷a;

(3)(ab) 5÷(ab)2; (4)(-a)7÷(-a)5

(5) (-b) 5÷(-b)2

Solution: (1) x8 ÷x2=x 8-2=x6.

(2)a4 ÷a =a 4-1=a3.

(3) (ab) 5÷(ab)2=(ab)5-2=(ab)3=a3b3.

(4)(-a)7÷(-a)5=(-a)7-5=(-a)2=a2

(5)(-b)5÷(-b)2=(-b)5-2=(-b)3=-b3

Explore

Fill in the blanks based on the meaning of division. What conclusion can you draw?

(1)32÷32= ( );

(2)103÷103= ( );

(3)am÷am=( )(a≠0).

Teach you a few tricks

1． The order of mixed operations of multiplication and division is the same as the order of mixed operations of rational numbers (i.e. "from left to right").

2. If the bases are different, first convert them to the same base and then apply the rule.

3. The entire algebraic expression can be regarded as the base.

4. If the operation result can be simplified, it should be simplified.

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For more information about the PPT courseware "Operations of Division of Integers with Powers of the Same Base", please click the "Operations of Division of Integers with Powers of the Same Base ppt" ppt tag.

"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:

"Division of Powers with the Same Base" PPT Part One: Preschool Preparation The intensity of the sound when a person speaks is usually 105, and the intensity of the sound when a motorcycle is driving is 1011. The intensity of the sound when a motorcycle is driving is the intensity of the sound when a person speaks. times? Solution: 10111..

"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..

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Update Time: 2024-10-08

This template belongs to Mathematics courseware Beijing Normal University seventh grade mathematics volume 2 industry PPT template

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