"Power of product and power of power" PPT courseware

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"Power of product and power of power" PPT courseware

1. Review: It is a pleasure to review the past and learn something new.

Multiplication of powers with the same base, base ____, exponent ______.

A power raised to a power has a base of _______ and an exponent of _______.

2. New Lesson: Climb high and look far, and walk hand in hand.

Discuss:

(1) What is 23×53? Communicate your practices with peers;

(2) What are the equivalents of 28 × 58 and 212 × 512?

(3) What rules did you discover from the above calculations? Let’s try another example.

Extension of formula

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

How to prove it?

(abc)n=an·bn·cn

Try the first method to prove:

There are two ideas______. One idea is to use the associative law of multiplication to convert the power of the product of three factors into the power of the product of two factors, and then use the multiplication rule of the product;

Another way of thinking is to still use the method of deriving the power of the product of two factors: the meaning of power, the commutative law and the associative law of multiplication.

Rules for multiplication of powers:

When raising powers, the base remains unchanged and the exponents are multiplied.

Notice:

1. The base a in the formula can be a specific number or an algebraic formula.

2. Note that when raising powers, the exponents are multiplied, while when multiplying powers with the same base, the exponents are added.

Example 1 Calculation:

(1)(106)2;

(2)(am)4(m is a positive integer);

(3)-(y3)2;

(4)(-x3)3．

Solution: (1)(106)2 = 106×2= 1012;

(2)(am)4 = am×4= a4m;

(3)-(y3)2 =-(y3×2)=-y6;

(4)(-x3)3 = -(x3)3= -(x3×3)=-x9．

think

1. If a2n=5, find a6n

2. If am=2, a2n=7, find a3m+4n

3 Compare the sizes of 2100 and 375.

4 Given that 44×83=2x, find the value of X.

Keywords: Teaching courseware for the power of products and powers, Qingdao edition seventh grade mathematics second volume PPT courseware download, seventh grade mathematics slide courseware download, power of products and powers PPT courseware download, .PPT format ;

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

"Power of product and power of power" PPT courseware 3:

"Power of product and power of power" PPT courseware 3 Review and think about the meaning of power: aa a=an The rule of multiplication of powers with the same base: am an=am+n (mn are all positive integers) The rule of multiplication of powers :(am)n=amn (m and n are both positive integers) Try your hand: Use powers..

"Power of product and power of power" PPT courseware 2:

"Powers of products and powers" PPT courseware 2 Think about it. Guess (am) what n is equal to? Is your guess correct? Generally speaking, (am)n=amamam=am+m++ m =amn. The rules for multiplication of powers: When raising powers, the base remains unchanged and the exponents are multiplied. Note: 1. male..

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Update Time: 2024-09-07

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