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"Powers to Powers and Products to Powers" Operations of Integers PPT Courseware 3
Knowledge review
1. Multiply powers with the same base
Rule: Multiply powers with the same base, keep the base unchanged, and add the exponents.
Mathematical symbols represent:
(where m and n are positive integers)
2. Power raised to the power
Rule: When raising powers, the base remains unchanged and the exponents are multiplied.
Mathematical notation: (am)n=amn
(where m and n are positive integers)
3. Power of product
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.)
Symbol representation:
(ab)n=anbn, where n is a positive integer;
(abc)n=anbncn where n is a positive integer.
Basic drill
Is the calculation below correct? If it's wrong, how to correct it?
(1) b5 · b5 = 2b5 ( ) (2) b5 + b5 = b10 ( )
b5 · b5= b10 b5 + b5 = 2b5
(3)x5 ·x5 = x25 ( ) (4) y5 · y5 = 2y10 ( )
x5 · x5 = x10 y5 · y5 =y10
(5)c · c3 = c3 ( ) (6) m + m3 = m4 ( )
c · c3 = c4 m + m3 = m + m3
(1) a ·a7- a4 ·a4 =____;
(2)(1/10)5 ×(1/10)3 =____;
(3)(-2 x2 y3)2 =____;
(4)(-2 x2 )3 =____;
Think about it:
1. Is the following calculation correct? If it is wrong, please correct it:
(1) (43)5=48 (2) (-28)3=(-2)24
(3) [(-3)5]3=-315 (4) (52)4×5=58
2. Give the reasons for each calculation step below and fill them in the brackets:
(p2)3.(p5)2
=p6.p10 ( )
=p6+10 ( )
=p16
1. Pay attention to symbol issues
Example 1 Determine whether the following equation is true:
① (-x)2＝-x2,
② (-x)3＝-x3,
③ (x-y)2=(y-x)2,
④ (x-y)3=(y-x)3,
⑤ x-a-b＝x-(a+b),
⑥x+a-b＝x-(b-a)．
Ability Challenge:
1. Compare size:
(-2) ×(-2)2× (-2)3×…× (-2)9× (-2)10 0.
2. It is known that the numbers a=2×103, b=3×104, c=5×105.
Then the value of a·b·c has ______ bits in the integer part.
3. If 10n×10m×10=1000, then n+m=_______.
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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.
"Powers to powers and products to powers" PPT courseware:
"Powers of Powers and Powers of Products" PPT Courseware Part One Content: Classroom Thoughts 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 4483=2x, find the value of X. Fill in the blanks for knowledge review: 1. am+am=___..
"Powers to Powers and Products to Powers" PPT:
"Powers of Powers and Powers of Products" PPT Part One Content: Knowledge Review an=aa a am an=am+n (m and n are both positive integers) Do (1) The side length of a cube is 102cm, What is its volume? (102)3=101010=102+2+2=106 (..
"Powers to Powers and Products to Powers" Operations of Integers PPT Courseware 2:
"Powers to Powers and Products to Powers" Operations on Integers PPT Courseware 2 Summary of the main differences between the three operations: Multiplication of powers with the same base: (1) Same base (2) Multiplication and combination of similar terms: (1) Same base Add the power of the same exponent (2): the form of exponentiation and then exponentiation..