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1.5 同底数幂的除法

幂. a n. 指数. 底数. 1.5 同底数幂的除法. 一种液体每升含有 10 12 个有害细菌,为了试验某种杀虫剂的效果,科学家们进行了实验,发现一滴杀虫剂可以杀死 10 9 个此种细菌。要将 1 升液体中的有害细菌全部杀死,需要这种杀虫剂多少滴?你是怎样计算的?. 10 12 ÷10 9 = ?. 解法一:原式 =. =. =10 3. 解法二:原式 =(10 3 ×10 9 ) ÷10 9. =10 3. 做一做. 计算下列各式,并说明理由 (m>n).

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1.5 同底数幂的除法

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  1. an 指数 底数 1.5同底数幂的除法

  2. 一种液体每升含有1012个有害细菌,为了试验某种杀虫剂的效果,科学家们进行了实验,发现一滴杀虫剂可以杀死109个此种细菌。要将1升液体中的有害细菌全部杀死,需要这种杀虫剂多少滴?你是怎样计算的?一种液体每升含有1012个有害细菌,为了试验某种杀虫剂的效果,科学家们进行了实验,发现一滴杀虫剂可以杀死109个此种细菌。要将1升液体中的有害细菌全部杀死,需要这种杀虫剂多少滴?你是怎样计算的?

  3. 1012 ÷109 = ? 解法一:原式= = =103 解法二:原式=(103×109) ÷109 =103

  4. 做一做 计算下列各式,并说明理由(m>n). (1)108 ÷105 (2) 10m ÷10n (3) (-3)m ÷(-3)n 解: 108 ÷105 =103 m-n m个10 =10×10 ×… ×10 =10m-n 10m ÷10n = n个10

  5. m个(-3) (-3)m ÷(-3)n = n个(-3) m-n =(-3)× (-3) ×… × (-3) = (-3) m-n

  6. 那么 am ÷an =? m个 a m-n = =a× a ×… × a = a m-n n个 a

  7. 同底数幂的除法法则 am ÷an =_______ (a≠0,m,n都是正整数,且m>n). 同底数幂相除,底数_______,指数_______. a m-n 不变 相减

  8. 例1 计算: (1)a7 ÷a4 (2)(-x)6 ÷ (-x)3 (3)(xy)4 ÷ (xy) (4)b2m+2 ÷b2 (5)(-x)5÷x3 (6) 98×272÷(-3)18 解:(1)a7 ÷a4 =a7-4 = a3 (2)(-x)6 ÷ (-x)3 = (-x)6-3 =(-x)3 = -x3 (3)(xy)4 ÷ (xy)= (xy)4-1= (xy)3 = x3y3 (4)b2m+2 ÷b2 = b2m+2-2= b2m (5)(-x)5÷x3=-x5÷x3=-x2 (6) 98×272÷(-3)18=316×36÷318=81

  9. 想一想 猜一猜 • =2 ( ) • =2 ( ) • =2 ( ) • =2( ) • 10000 =104 • =10( ) • =10( ) • 10 =10( ) 16 =24 8 =2( ) 4 =2( ) 2 =2( ) 3 3 2 2 1 1 0 0 -1 • =10 ( ) • 0.1 =10 ( ) • 0.01 =10 ( ) • 0.001 =10( ) -1 -2 -2 -3 -3

  10. a-p= (a≠0,p是正整数) 我们规定: a0 = 1 (a≠0)

  11. 解(1) 10-3 = = =0.001 (2) 70 × 8-2 = 1× = (3)1.6 × 10-4 =1.6× =1.6×0.0001=0.00016 例2 用小数或分数表示下列各数 (1)10-3 (2) 70 × 8-2(3)1.6 × 10-4

  12. -3x+y+4z=1 , 得方程组 2x-2y-z=0 , y-z=0 . x=3 , 解得 y=2 , z=2 . 解:原等式可化为 32x·2-3x·2y·5y·3-2y·24z·3-z·5-z=2 , 即 2-3x+y+4z·32x-2y-z·5y-z=21×30×50 .

  13. 课堂练习: 下面的计算是否正确?如有错误请改正. (1) a6÷a=a6 ; (2) b6÷b3=b2 ; (3) a10÷a9=a ; (4) (-bc)4÷(-bc)2=-b2c2 .

  14. 作业: ⒈ 阅读课本P19-21; ⒉ P21 习题 1.7 1 , 3,4 ; ⒊ KKL; ⒋ JZST.

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