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"Multiplication of powers with the same base" PPT courseware 3
The manned space flight of the spacecraft is a great feat of our country’s aerospace industry. It flies at a speed of about 104 meters/second and flies for about 105 seconds per day. Approximately how many meters does it fly every day?
Solution: 104×105=109 (meters)
Answer: It flies about 109 meters every day.
think:
What does an mean? What are a, n, and an called respectively?
Try it, do you remember it?
1. 2×2×2=2( )
2. a·a·a·a·a = a( )
3. a·a • · · · • a = a( )
learning target
1. Go through the process of exploring the operational properties of multiplication of powers with the same base, and further understand the meaning of power.
2. Be able to recognize powers with the same base and multiplication of powers with the same base through examples.
3. Be able to correctly use the multiplication properties of powers with the same base to perform calculations.
Give it a try, discuss it
1. Can you write an expression for multiplying powers with the same base?
2. Can you find the rule of multiplying powers with the same base?
And share your findings with the group.
collaborative inquiry
Please ask students to fill in the blanks below based on their understanding of the meaning of exponentiation.
(1) 25×22 = (2 × 2 ×2×2× 2) ×(2 × 2)
= 2×2 ×2 × 2×2×2×2=2( );
(2)a3×a2 = (a×a×a) ×(a×a)
=a×a×a×a×a= a();
(3) 5m · 5n=(5×···×5) ×(5×···×5) = 5(m+n).
Thinking: Observe the left and right sides of each question above. What is the relationship between the base and the exponent?
Conjecture: am · an= am+n (when m and n are both positive integers)
Multiplication formula for powers with the same base:
am · an = am+n (m and n are both positive integers)
When powers with the same base are multiplied, the base remains unchanged and the exponents are added.
Thinking: When three or more powers with the same base are multiplied, does the multiplication formula for powers with the same base also apply? How to express it with formula?
Fierce eyes and golden eyes
Is the calculation below correct? If it's wrong, how to correct it?
(1) a · a2 = a2 ( ) (2 ) x2 · y5 = xy7 ( )
(3) a + a2 = a3 ( ) (4) a3 · a3 = a9 ( )
(5) a3+a3 = a6 ( ) (6) a3 · a3 = a6 ( )
1. 25× 125 = 5x, then x =5;
2. m6=m( ) ·m( ), can you give several different filling methods?
① m6=m ·m5 ② m6=m2·m4 ③ m6=m3·m3
3. Given that 2m=5 and 2n=16, find the value of 2m+n.
adapt to changing circumstances
1. Fill in the blanks:
(1)x5 ·( )=x 8 (2)a ·( )=a6
(3) x · x3 ( ) = x7 (4) xm · ( ) = x3m
2. Fill in the blanks:
(1) 8 = 2x, then x =______;
(2) 8× 4 = 2x, then x =______;
(3) 3×27×9 = 3x, then x =______.
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"Multiplication of powers with the same base" PPT download:
"Multiplication of Powers with the Same Base" PPT Download Part One: Classroom Questions Question: An electronic computer can perform 1014 operations per second. How many operations can it perform in 103 seconds? 1014103＝(1010)(101010)＝（101010）＝1017 That is:..
"Multiplication of powers with the same base" PPT:
"Multiplication of Powers with the Same Base" PPT Part One: Knowledge Reproduction Can you tell the meaning of an? Represents the operation of the product of n a's. Fill in the blanks: 1. 2222=2 ( ) 2. aaaaaa=a ( ) 3. aaaa=a ( ) Summary rule The multiplication rule for powers with the same base: ..
"Multiplication of powers with the same base" PPT courseware 2:
"Multiplication of Powers with the Same Base" PPT Courseware 2 Question Scenario An electronic computer can perform 1014 operations per second. How many operations can it perform in 103 seconds? Column formula: 1014103 How to calculate 1014103? Knowledge Review 1. What is exponentiation? Find a few that are the same...