人教版八年数学上幂的乘方教学设计PPT.ppt

活动 1 知识回顾口述同底数幂的乘法法则 a m· a n = a m+n (m、n都是正整数). 同底数幂相乘, 底数不变,指数相加. 5399? 26aa? 53)()(xx??? 33)(xx?? 432xxx??aaaa??? 432 89? 8a? 8x? 6x?? 9x? 52a?(1); (3); (5);(6). (2); (4); 计算: 一个正方体的棱长是 10, 它的体积是多少? 如果它的棱长是 10 2,它的体积又是多少?如果是 10 4呢? 10 3 =10 × 10 × 10 (10 2) 3 (10 4) 3 =10 6 =10 12 =10 2× 10 2× 10 2 =10 4× 10 4× 10 4怎样计算? (1)(3 2) 3 =( ) × ( ) × ( )=3 ( ) (2)(a 2) 3 =( ) × ( ) × ( )=a ( ) (3)(a m) 3 =( ) × ( ) × ( )=a ( ) (m 为正整数) 根据乘方的意义与同底数幂的乘法填空, 看看计算的结果有什么规律? 3 23 23 2 66a 2a 2a 2a ma ma m 3m (3 2) 3=3 2×3 =3 6 (a 2) 3=a 2×3 =a 6 (a m) 3=a m×3 =a 3m 对于任意底数 a与任意正整数 m、n (4)( a m) n =a m·a m…· a m =a m+m+ …+m =a mn n个a m n 个m 幂的乘方运算法则(a m) n=a mn(m,n都是正整数) 即幂的乘方, 底数不变,指数相乘. 例计算: (1)(10 3) 5 (2)(a 4) 2 (3)(a m) 2 (4)-( X 4) 3解: (1) (10 3) 5 =10 3×5 =10 15 (2) (a 4) 2 =a 4×4 =a 16 (3) (a m) 2 =a m×2 =a 2m (4) -(X 4) 3 =-X 4×3 =-X 12 下面计算是否正确?如有错误请改正。(1)X 3·X 3 =2X 3 (2) X 2 +X 2 =X 4 (3) a 4·a 2 =a 6 (4) (a 3) 7 =a 10 (5 ) (X 5) 3 =X 15 (6)-(a 3) 4 =a 12√√× ×× × X 3·X 3 =X 6X 2 +X 2 =2X 2 (a 3) 7 =a 21 -(a 3) 4 =-a 12 例2把 42]) [(yx?化成 nyx)(?的形式. 解: 42 42)(]) [( ????yxyx 8)(yx??幂的乘方的逆运算: (1) x 13·x 7=x () =( ) 5 =( ) 4 =( ) 10; (2) a 2m =( ) 2 =( ) m(m为正整数) . 20x 4x 5x 2a ma 2 mn nm mnaaa)()(?????幂的乘方法则的逆用例计算: (1) (X 2) m+1 (2)[-(X-Y) 5] 2 (3) –(a 2) 3· (a 4) 3 (4)(X 2) 2·X 4 +(X 2) 4 (1) (X 2) m+1 =X 2 (m+1) =X 2m+2 (2)[-(X-Y) 5] 2 =(X-Y) 5×2 =(X-Y) 10 (3) –(a 2) 3· (a 4) 3=–a 6·a 12=–a 18 (4)(X 2) 2·X 4 +(X 2) 4 =X 4·X 4 +X 8 =X 8 +X 8 =2X 8 解: