7班数学
问题1:利用指数定律简化并将答案写成指数形式:
(一)' 3^2 xx 3^4 xx 3^8 '
答:' 3^2 xx 3^4 xx 3^8 '
' = 3^(2 + 4 + 8) = 3^14 '
(b)' 6^15 ÷ 6^10 '
答:' 6^15 ÷ 6^10 = 6^(15 - 10) = 6^5 '
(c)' a^3 xx a^2 '
答:' a^3 × a^2 = a^(3 + 2) = a^5 '
(d)' 7^x \xx 7^2 '
答:' 7^x \xx 7^2 = 7^(x + 2) '
(e)' (5^2)^3 × 5^3 '
答:' (5^2)^3 × 5^3 = 5^6 × 5^3 '
' = 5^(6 + 3)= 5^9 '
(f)' 2^5 × 5^5 '
答:' 2^5 xx 5^5x = (2xx 5)^5 = 10^5 '
(g)' a^4 xx b^4 '
答:' a^4 xx b^4 = (ab)^4 '
(h)“(3 ^ 4)^ 4”
答:' (3^4)^4 = 3^16 '
(我)' (2^20 ÷ 2^15) xx 2^3 '
答:' (2^20 ÷ 2^15) xx ^3 = [2^(20 - 15)] xx ^3 '
' = 2^5 × 2^3 = 2^(5 + 3) = 2^8 '
(j)“8 t÷8 ^ ^ 2”
答:' 8^t ÷ 8^2 = 8^(t - 2) '
问题2:将下列每一项简化并以指数形式表示:
(一)”(2 ^ 3 xx3 ^ 4 xx4) / (3 xx32) '
答:' = (2 ^ 3 xx3 ^ 4 xx2 ^ 2) / (3 xx2 ^ 5)”
' = (2 ^ (3 + 2) xx3 ^ 4) / (3 xx2 ^ 5)”
' = (2 ^ 5 xx3 ^ (4 - 1)) / (2 ^ 5) '
= 2 ^(盘中)xx3 ^ 3 = 2 ^ 0 xx3 ^ 3 = 3 ^ 3 '
(b)”((5 ^ 2)^ 3 xx5 ^ 4)÷5 ^ 7”
答:' = (5 ^ 6 xx5 ^ 4)÷5 ^ 7”
' =(5 ^(6 + 4)÷5 ^ 7 = 5 ^ ^ 5(10)÷7”
' = 5 ^(10 - 7)结果= 5 ^ 3 '
(c)”(3 xx7 ^ 2 xx11 ^ 8) / (21 xx11 ^ 3)”
答:' = (3 xx7 ^ 2 xx11 ^ 8) / (3 xx7xx11 ^ 3)”
= 3 ^ (1 - 1) xx7 ^ (2 - 1) xx11 ^ (8 - 3)
' = 3 ^ 0 xx7 ^ 1 xx11 ^ 5 = 7 xx11 ^ 5 '
(d)”(3 ^ 7)/ (3 ^ 4 xx3 ^ 3)”
答:' = (3 ^ 7) / (3 ^ (4 + 3)) = (3 ^ 7) / (3 ^ 7) '
' = 3 ^(7) = 3 ^ 0 = 1”
(e)' 2 ^ 0 + 3 ^ 0 + 4 ^ 0 '
答:“= 1 + 1 + 1 = 3”
(f)' 2 ^ 0 xx3 xx4 ^ 0 ^ 0 '
答:“= 1 xx1xx1 = 1”
(g)”(3 + 2 ^ ^ 0 0)xx5 ^ 0 '
答:' =(1 + 1)民= 2民= 2》
(h)”(2 ^ 8 xxa ^ 5) / (4 ^ 3 xxa ^ 3)”
答:' = (2 ^ 8 xxa ^ (5 - 3)) / ((2 ^ 2) ^ 3) '
' = (2 ^ 8 xxa ^ 2) /(2 ^ 6) = 2 ^(之后)xxa ^ 2》
' = 2 ^ 2 xxa ^ 2 =(2) ^ 2”
(我)”(4 ^ 5 xxa ^ 8 b ^ 3) / (4 ^ 5 xxa ^ 5 b ^ 2)”
答:= 4 ^(盘中)xxa ^ (8 - 5) xxb ^ (3 - 2)
' = 4 ^ 0 xxa xxb ^ 3 ^ 1 = ^ 3 b”
(j)“(2 ^ 3 xx2) ^ 2”
答:' = 2 ^ (3 xx2) xx2 ^ 2 = 2 ^ 6 xx2 ^ 2》
' = 2 ^ (6 + 2) = 2 ^ 8 '
问题3:说出对或错，并证明你的答案:
问题4:将下列每一项仅以指数形式表示为质因数的乘积:
(一)' 108 xx 192 '
答:' 108 xx 192 ' ' = (2 xx 2 xx 3 xx 3 xx 3) xx (2 xx 2 xx 2 xx 2 xx 2 xx 2 xx 3) '
' = 2 ^ 2 xx 3 ^ 3 xx 2 ^ 6 xx 3 ' ' = 2 ^ 3 ^ (2 + 6) xx (3 + 1) = 2 ^ 8 xx 3 ^ 4 '
(b) 270
答:' 270 = 2 xx 3^3 xx 5 '
(c)' 729 xx 64 '
答:' 729 xx 64 = 3^6 xx 2^8 '
(d) 768
答:' 768 = 2^8 × 3 '
问题5:简化
(一)”((2 ^ 5)^ 2 xx7 ^ 3) / (8 ^ 3 xx7) '
答:' = (2 ^ (5 xx2) xx7 ^ (3 - 1)) / ((2 ^ 3) ^ 3) '
' = (2 ^ (10) xx7 ^ 2) / (2 ^ 9) = 2 ^ (- 9) xx7 xx7 ^ 2 = 2 ^ 2》
(b)”(25 xx5 ^ 2 xxt ^ 8) / (8 ^ 3 xxt ^ 4)”
答:' = (5 ^ 2 xx5 ^ 2 xxt ^ (8 - 4) / ((2 ^ 3) ^ 3) '
' = (5 ^ (2 + 2) xxt ^ 4) / (2 ^ 9) = (5 ^ 4 xxt ^ 4) / (2 ^ 9) '
(c)”(3 ^ 5 xx10 ^ 5 xx25) / (5 ^ 7 xx6 ^ 5)”
答:' = (3 ^ 5 5 xx5 xx (2 xx5) ^ ^ 2) / (5 ^ 7 xx (2 xx3) ^ 5)”
' = (3 ^ 5 xx2 ^ 5 xx5 ^ 5 xx5 ^ 2) / (5 ^ 7 xx2 ^ 5 xx3 ^ 5)”
= 3 ^(盘中)xx2 ^(盘中)xx5 ^(5 + 2 - 7日)
' = 3 ^ 0 xx2 xx5 ^ 0 ^ 0 = 1”
半岛公司背景