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15.2.3,整数指数幂,八年级 上册,正整数指数幂有以下运算性质：,（,6,）,0,指数幂的运算,:,当,a0,时，,a,0,=1,。,复习,（,1,）,同底数幂的乘法：,a,m,a,n,=,a,m+n,(a0 m,、,n,为正整数,),（,2,）,幂的乘方：,(,a,m,),n,=,a,mn,(a0 m,、,n,为正整数,),（,3,）,积的乘方：,(,ab),n,=,a,n,b,n,(a,，,b0 m,、,n,为正整数,),（,4,）,同底数幂的除法：,a,m,a,n,=a,m-n,(,a0 m,、,n,为正整数且,mn,),（,5,）,分式的乘方,:,（,b0,，,n,是正整数）,a,m,a,n,=a,m-n,(a0 m,、,n,为正整数且,mn,),a,5,a,3,=a,2,a,3,a,5,=,？,分,析,a,3,a,5,=a,3-5,=a,-2,a,3,a,5,=,=,n,是正整数时,a,-n,属于分式。并且,(a0),例如,:,引入负整数指数幂后，指数的取值范围就扩大到全体整数。,a,m,=,a,m,(m,是正整数）,1,（,m=0,）,（,m,是负整数）,这就是说：,a,-n,(a0),是,a,n,的倒数。,（,1,）,3,2,=_,，,3,0,=_,，,3,-2,=_;,（,2,）,(-3),2,=_,，,(-3),0,=_,，,(-3),-2,=,_,；,（,3,）,b,2,=_,b,0,=_,b,-2,=_(b0).,练,习,9,1,9,1,b,2,1,a,3,a,-5,=,a,-3,a,-5,=,a,0,a,-5,=,a,-2,a,-8,a,-5,a,m,a,n,=,a,m+n,，这条性质对于,m,，,n,是任意整数的情形仍然适用。,归,纳,整数指数幂有以下运算性质：,（,1,）,a,m,a,n,=,a,m+n,(a0),（,2,）,(,a,m,),n,=,a,mn,(a0),（,3,）,(,ab),n,=,a,n,b,n,(a,b0),（,4,）,a,m,a,n,=a,m-n,(a0),（,5,）（,b0,）,当,a0,时，,a,0,=1,。,（,6,）,a,-3,a,-9,=,(a,-3,),2,=,(ab),-3,=,a,-3,a,-5,=,a,-12,a,-6,a,-3,b,-3,a,-3-(-5),=a,2,例题：,(1)(a,-1,b,2,),3,;,(2)a,-2,b,2,(a,2,b,-2,),-3,跟踪练习：,(1)x,2,y,-3,(x,-1,y),3,；,(2)(2ab,2,c,-3,),-2,(a,-2,b),3,(3)2a,-2,b,2,（2a,-1,b,-2,）,-3,(3),小结,a,m,a,n,=,a,m+n,(,a,m,),n,=,a,mn,(,ab),n,=,a,n,b,n,运算法则,（,m，n,为,整数,a,0，b,0）,a,0,=1,(a,0),规定,课后作业,基础题：,1.,计算：,(a+b),m+1,(a+b),n-1,;(2)(-a,2,b),2,(-a,2,b,3,),3,(-ab,4,),5,(3)(x,3,),2,(x,2,),4,x,0,(4)(-1.8x,4,y,2,z,3,)(-0.2x,2,y,4,z)(-1/3xyz),提高题：,2.,已知 ，求,a,51,a,8,的值；,3.,计算：,x,n+2,x,n-2,(x,2,),3n-3,;,4.,已知：,10,m,=5,10,n,=4,求,10,2m-3n,.,科学计数法,光速约为,310,8,米,/,秒,太阳半径约为,6.9610,5,千米,目前我国人口约为,6.110,9,小于,1,的数也可以用科学计数法表示。,a10,-n,a,是整数位只有一位的正数，,n,是正整数。,0.00001=10,-5,0.0000257=2.5710,-5,(1)0.005,0.005,0.005=5 10,-3,小,数点,原本的位置,小,数点,最,后,的位,置,小,数点,向右,移了,3,位,例,3,用科学记数法表示下列各数,：,(2)0.020 4,0.02 04,0.020 4=2.04,10,-2,小,数点,原本的位置,小,数点,最,后,的位置,小,数点,向右,移了,2,位,(3)0.000 36,0.000 36,0.000 36=3.6,10,-4,小,数点,原本的位置,小,数点,最,后,的位置,小,数点,向右,移了,4,位,对于一个小于,1,的正小数，如果小数点后至第一个非,0,数字前有,8,个,0,，用科学计数法表示这个数时，,10,的指数是多少？如果有,m,个,0,呢？,思,考,0.000 000 0027=_,，,0.000 000 32=_,，,0.000 000,001=_,，,m,个,0,2.710,-9,3.210,-7,10,-(m+1),1.,用科学计数法表示下列数：,0.000 000 001,，,0.001 2,，,0.000 000 345,，,-0.000 03,，,0.000 000 010 8 3780 000,1,纳米,=10,-9,1,亿,=10,8,课 堂 练 习,基础题,2.,计算：,(210,-6,)(3.210,3,);,(2)(210,-6,),2,(10,-4,),3,3.,（,提高题,）用科学计数法把,0.000009405,表示成,9.40510,n,，那么,n=_.,小,结,（,1,）,n,是正整数时,a,-n,属于分式。并且,(a0),（,2,）科学计数法表示小于,1,的小数：,a10,-n,（,a,是整数位只有一位的正数，,n,是正整数。）,
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