6.5E：练习
- Page ID
- 204968
练习成就完美
使用指数的商属性简化表达式
在以下练习中，简化。
- \(\dfrac{x^{18}}{x^{3}}\)
- \(\dfrac{5^{12}}{5^{3}}\)
- \(\dfrac{y^{20}}{y^{10}}\)
- \(\dfrac{7^{16}}{7^{2}}\)
- 回答
-
- \(y^{10}\)
- \(7^{14}\)
- \(\dfrac{p^{21}}{p^{7}}\)
- \(\dfrac{4^{16}}{4^{4}}\)
- \(\dfrac{u^{24}}{u^{3}}\)
- \(\dfrac{9^{15}}{9^{5}}\)
- 回答
-
- \(u^{21}\)
- \(9^{10}\)
- \(\dfrac{q^{18}}{q^{36}}\)
- \(\dfrac{10^{2}}{10^{3}}\)
- \(\dfrac{t^{10}}{t^{40}}\)
- \(\dfrac{8^{3}}{8^{5}}\)
- 回答
-
- \(\dfrac{1}{t^{30}}\)
- \(\dfrac{1}{64}\)
- \(\dfrac{b}{b^{9}}\)
- \(\dfrac{4}{4^{6}}\)
- \(\dfrac{x}{x^{7}}\)
- \(\dfrac{10}{10^{3}}\)
- 回答
-
- \(\dfrac{1}{x^{6}}\)
- \(\dfrac{1}{100}\)
使用零指数简化表达式
在以下练习中，简化。
- \(20^{0}\)
- \(b^{0}\)
- \(13^0\)
- \(k^{0}\)
- 回答
-
- 1
- 1
- \(-27^{0}\)
- \(-\left(27^{0}\right)\)
- \(-15^{0}\)
- \(-\left(15^{0}\right)\)
- 回答
-
- −1
- −1
- \((25 x)^{0}\)
- \(25 x^{0}\)
- \((6 y)^{0}\)
- \(6 y^{0}\)
- 回答
-
- 1
- 6
- \((12 x)^{0}\)
- \(\left(-56 p^{4} q^{3}\right)^{0}\)
- 7\(y^{0}(17 y)^{0}\)
- \(\left(-93 c^{7} d^{15}\right)^{0}\)
- 回答
-
- 7
- 1
- \(12 n^{0}-18 m^{0}\)
- \((12 n)^{0}-(18 m)^{0}\)
- \(15 r^{0}-22 s^{0}\)
- \((15 r)^{0}-(22 s)^{0}\)
- 回答
-
- −7
- 0
使用商乘方属性简化表达式
在以下练习中，简化。
- \(\left(\dfrac{3}{4}\right)^{3}\)
- \(\left(\dfrac{p}{2}\right)^{5}\)
- \(\left(\dfrac{x}{y}\right)^{6}\)
- \(\left(\dfrac{2}{5}\right)^{2}\)
- \(\left(\dfrac{x}{3}\right)^{4}\)
- \(\left(\dfrac{a}{b}\right)^{5}\)
- 回答
-
- \(\dfrac{4}{25}\)
- \(\dfrac{x^{4}}{81}\)
- \(\left(\dfrac{a}{b}\right)^{5}\)
- \(\left(\dfrac{a}{3 b}\right)^{4}\)
- \(\left(\dfrac{5}{4 m}\right)^{2}\)
- \(\left(\dfrac{a}{3 b}\right)^{4}\)
- \(\left(\dfrac{10}{3 q}\right)^{4}\)
- 回答
-
- \(\dfrac{x^{3}}{8 y^{3}}\)
- \(\dfrac{10,000}{81 q^{4}}\)
通过应用多个属性来简化表达式
在以下练习中，简化。
\(\dfrac{\left(a^{2}\right)^{3}}{a^{4}}\)
\(\dfrac{\left(p^{3}\right)^{4}}{p^{5}}\)
- 回答
-
\(p^{7}\)
\(\dfrac{\left(y^{3}\right)^{4}}{y^{10}}\)
\(\dfrac{\left(x^{4}\right)^{5}}{x^{15}}\)
- 回答
-
\(x^{5}\)
\(\dfrac{u^{6}}{\left(u^{3}\right)^{2}}\)
\(\dfrac{v^{20}}{\left(v^{4}\right)^{5}}\)
- 回答
-
1
\(\dfrac{m^{12}}{\left(m^{8}\right)^{3}}\)
\(\dfrac{n^{8}}{\left(n^{6}\right)^{4}}\)
- 回答
-
\(\dfrac{1}{n^{16}}\)
\(\left(\dfrac{p^{9}}{p^{3}}\right)^{5}\)
\(\left(\dfrac{q^{8}}{q^{2}}\right)^{3}\)
- 回答
-
\(q^{18}\)
\(\left(\dfrac{r^{2}}{r^{6}}\right)^{3}\)
\(\left(\dfrac{m^{4}}{m^{7}}\right)^{4}\)
- 回答
-
\(\dfrac{1}{m^{12}}\)
\(\left(\dfrac{p}{r^{11}}\right)^{2}\)
\(\left(\dfrac{a}{b^{6}}\right)^{3}\)
- 回答
-
\(\dfrac{a^{3}}{b^{18}}\)
\(\left(\dfrac{w^{5}}{x^{3}}\right)^{8}\)
\(\left(\dfrac{y^{4}}{z^{10}}\right)^{5}\)
- 回答
-
\(\dfrac{y^{20}}{z^{50}}\)
\(\left(\dfrac{2 j^{3}}{3 k}\right)^{4}\)
\(\left(\dfrac{3 m^{5}}{5 n}\right)^{3}\)
- 回答
-
\(\dfrac{27 m^{15}}{125 n^{3}}\)
\(\left(\dfrac{3 c^{2}}{4 d^{6}}\right)^{3}\)
\(\left(\dfrac{5 u^{7}}{2 v^{3}}\right)^{4}\)
- 回答
-
\(\dfrac{625 u^{28}}{16 v^{12}}\)
\(\left(\dfrac{k^{2} k^{8}}{k^{3}}\right)^{2}\)
\(\left(\dfrac{j^{2} j^{5}}{j^{4}}\right)^{3}\)
- 回答
-
\(j^{9}\)
\(\dfrac{\left(t^{2}\right)^{5}\left(t^{4}\right)^{2}}{\left(t^{3}\right)^{7}}\)
\(\dfrac{\left(q^{3}\right)^{6}\left(q^{2}\right)^{3}}{\left(q^{4}\right)^{8}}\)
- 回答
-
\(\dfrac{1}{q^{8}}\)
\(\dfrac{\left(-2 p^{2}\right)^{4}\left(3 p^{4}\right)^{2}}{\left(-6 p^{3}\right)^{2}}\)
\(\dfrac{\left(-2 k^{3}\right)^{2}\left(6 k^{2}\right)^{4}}{\left(9 k^{4}\right)^{2}}\)
- 回答
-
64\(k^{6}\)
\(\dfrac{\left(-4 m^{3}\right)^{2}\left(5 m^{4}\right)^{3}}{\left(-10 m^{6}\right)^{3}}\)
\(\dfrac{\left(-10 n^{2}\right)^{3}\left(4 n^{5}\right)^{2}}{\left(2 n^{8}\right)^{2}}\)
- 回答
-
−4,000
划分单项式
在以下练习中，将单项式分开。
56\(b^{8} \div 7 b^{2}\)
63\(\nu^{10} \div 9 v^{2}\)
- 回答
-
7\(v^{8}\)
\(-88 y^{15} \div 8 y^{3}\)
\(-72 u^{12} \div 12 u^{4}\)
- 回答
-
\(-6 u^{8}\)
\(\dfrac{45 a^{6} b^{8}}{-15 a^{10} b^{2}}\)
\(\dfrac{54 x^{9} y^{3}}{-18 x^{6} y^{15}}\)
- 回答
-
\(-\dfrac{3 x^{3}}{y^{12}}\)
\(\dfrac{15 r^{4} s^{9}}{18 r^{9} s^{2}}\)
\(\dfrac{20 m^{8} n^{4}}{30 m^{5} n^{9}}\)
- 回答
-
\(\dfrac{-2 m^{3}}{3 n^{5}}\)
\(\dfrac{18 a^{4} b^{8}}{-27 a^{9} b^{5}}\)
\(\dfrac{45 x^{5} y^{9}}{-60 x^{8} y^{6}}\)
- 回答
-
\(\dfrac{-3 y^{3}}{4 x^{3}}\)
\(\dfrac{64 q^{11} r^{9} s^{3}}{48 q^{6} r^{8} s^{5}}\)
\(\dfrac{65 a^{10} b^{8} c^{5}}{42 a^{7} b^{6} c^{8}}\)
- 回答
-
\(\dfrac{65 a^{3} b^{2}}{42 c^{3}}\)
\(\dfrac{\left(10 m^{5} n^{4}\right)\left(5 m^{3} n^{6}\right)}{25 m^{7} n^{5}}\)
\(\dfrac{\left(-18 p^{4} q^{7}\right)\left(-6 p^{3} q^{8}\right)}{-36 p^{12} q^{10}}\)
- 回答
-
\(\dfrac{-3 q^{5}}{p^{5}}\)
\(\dfrac{\left(6 a^{4} b^{3}\right)\left(4 a b^{5}\right)}{\left(12 a^{2} b\right)\left(a^{3} b\right)}\)
\(\dfrac{\left(4 u^{2} v^{5}\right)\left(15 u^{3} v\right)}{\left(12 u^{3} v\right)\left(u^{4} v\right)}\)
- 回答
-
\(\dfrac{5 v^{4}}{u^{2}}\)
混合练习
- \(24 a^{5}+2 a^{5}\)
- \(24 a^{5}-2 a^{5}\)
- 24\(a^{5} \cdot 2 a^{5}\)
- 24\(a^{5} \div 2 a^{5}\)
- \(15 n^{10}+3 n^{10}\)
- \(15 n^{10}-3 n^{10}\)
- 15\(n^{10} \cdot 3 n^{10}\)
- 15\(n^{10} \div 3 n^{10}\)
- 回答
-
- 18\(n^{10}\)
- 12\(n^{10}\)
- 45\(n^{20}\)
- 5
- \(p^{4} \cdot p^{6}\)
- \(\left(p^{4}\right)^{6}\)
- \(q^{5} \cdot q^{3}\)
- \(\left(q^{5}\right)^{3}\)
- 回答
-
- \(q^{8}\)
- \(q^{15}\)
- \(\dfrac{y^{3}}{y}\)
- \(\dfrac{y}{y^{3}}\)
- \(\dfrac{z^{6}}{z^{5}}\)
- \(\dfrac{z^{5}}{z^{6}}\)
- 回答
-
- z
- \(\dfrac{1}{z}\)
\(\left(8 x^{5}\right)(9 x) \div 6 x^{3}\)
\((4 y)\left(12 y^{7}\right) \div 8 y^{2}\)
- 回答
-
6\(y^{6}\)
\(\dfrac{27 a^{7}}{3 a^{3}}+\dfrac{54 a^{9}}{9 a^{5}}\)
\(\dfrac{32 c^{11}}{4 c^{5}}+\dfrac{42 c^{9}}{6 c^{3}}\)
- 回答
-
15\(c^{6}\)
\(\dfrac{32 y^{5}}{8 y^{2}}-\dfrac{60 y^{10}}{5 y^{7}}\)
\(\dfrac{48 x^{6}}{6 x^{4}}-\dfrac{35 x^{9}}{7 x^{7}}\)
- 回答
-
3\(x^{2}\)
\(\dfrac{63 r^{6} s^{3}}{9 r^{4} s^{2}}-\dfrac{72 r^{2} s^{2}}{6 s}\)
\(\dfrac{56 y^{4} z^{5}}{7 y^{3} z^{3}}-\dfrac{45 y^{2} z^{2}}{5 y}\)
- 回答
-
\(-y z^{2}\)
日常数学
内存一兆\(10^6\)字节约为字节。 一千兆\(10^9\)字节约为字节。 一千兆字节中有多少兆字节？
内存一千兆\(10^9\)字节约为字节。 一太\(10^12\)字节大约等于字节。 一太字节中有多少千兆字节？
- 回答
-
\(10^{3}\)
写作练习
詹妮弗认为商数\(\dfrac{a^{24}}{a^{6}}\)简化为她的推理\(a^{4} .\)有什么问题？
莫里斯\(\dfrac{d^{7}}{d}\)通过写下他的推理\(\dfrac{\not{d}^7}{\not{d}}=7 .\)有什么问题来简化商数？
- 回答
-
答案会有所不同。
当 Drake 简化后\(-3^{0}\)，\((-3)^{0}\)他得到了同样的答案。 解释如何正确使用操作顺序给出
不同的答案。
罗伯特认为\(x^{0}\)简化为 0。 你会说什么来说服罗伯特他错了？
- 回答
-
答案会有所不同。
自检
a. 完成练习后，使用此清单评估您对本节目标的掌握程度。
b. 在 1-10 分中，根据你在清单上的回答，你会如何评价你对本节的掌握程度？ 你怎么能改善这个？