"Powers to Powers and Products to Powers" Operations of Integers PPT Courseware 2

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"Powers to Powers and Products to Powers" Operations of Integers PPT Courseware 2

The main differences between the three operations

Induction: Multiplying powers with the same base: (1) Multiplying powers with the same base (2)

Combine similar items: (1) Same base and same exponent (2) Addition

Power raised to a power: the form of exponentiation and then exponentiation

Explore & communicate

(1) According to the definition of power (the meaning of power), what does (ab)3 represent?

(2) In order to calculate (simplify) the expression ab·ab·ab, the commutative law and associative law of multiplication can be applied. In what form can it be written?

(3) Starting from the special (ab)3=a3b3, can you think of a general formula?

(ab)3=ab·ab·ab=a·a·a · b·b·b=a3·b3

multiplication rule for products

(ab)n = an·bn (m,n are both positive integers)

Rule: To raise the power of a product, first multiply each factor in the product to the power, and then multiply the resulting powers together. (That is, equal to the product of the powers of the factors in the product.)

Can you tell the meaning of the word "factor" in the law?

(a+b)n, can it be calculated using the multiplication rule of products?

That is, is "(a+b)n= an·bn" true?

Also, is "(a+b)n= an+an" true?

Extension of formula

Does the power of three or more products also have the above properties? How to express it with a formula?

(abc)n=an·bn·cn

[Example 2] Calculation:

(1)(3x)2; (2)(-2b)5; (3)(-2xy)4; (4)(3a2)n.

Practice in class

1. Calculation:

(1) (- 3n)3; (2) (5xy)3; (3) –a3 +(–4a)2 a .

What did you learn in this lesson?

The meaning of power: n a a·a·…·a=an

Rules for multiplication of powers with the same base: am · an=am+n

Rule of exponentiation: (ab)n=anbn

The product raised to the power = the product of each factor raised to the power.

In reverse, use am · an =am+n, (am)n =amn, an·bn=(ab)n

Can make some calculations simple.

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For more information about the PPT courseware "Operations of Powers and Products Powered by Integers" PPT courseware, please click the Power of Powers and Products Powered ppt Operations of Integers ppt tag.

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Update Time: 2024-09-19

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