Bài 1:
\(a,\left(-3\right)^3+125\cdot\left[\left(\dfrac{3}{4}\right)^3:\left(\dfrac{5}{4}\right)^3\right]\)
\(=\left(-3\right)^3+125\cdot\left[\left(\dfrac{3}{4}:\dfrac{5}{4}\right)^3\right]\)
\(=\left(-3\right)^3+125\cdot\left[\left(\dfrac{3}{4}\cdot\dfrac{4}{5}\right)^3\right]\)
\(=\left(-3\right)^3+125\cdot\left[\left(\dfrac{3}{5}\right)^3\right]\)
\(=-27+125\cdot\dfrac{27}{125}\)
\(=-27+27=0\)
\(b,2^3+3\cdot\left(\dfrac{1}{2}\right)^0-1+\left[\left(-2\right)^2:\dfrac{1}{8}\right]-9\)
\(=8+3\cdot1-1+\left[4:\dfrac{1}{8}\right]-9\)
\(=8+3\cdot1-1+\left[4\cdot8\right]-9\)
\(=8+3-1+32-9\)
\(=11-1+32-9\)
\(=10+32-9\)
`= 42 - 9 = 33`
Bài `2`
\(a,\left(-\dfrac{4}{9}\right)^{13}\cdot\left(\dfrac{-4}{9}\right)^{13}\)
\(=\left(-\dfrac{4}{9}\right)^{13}\cdot\left(-\dfrac{4}{9}\right)^{13}\)
\(=\left(-\dfrac{4}{9}\right)^{13+13}=\left(-\dfrac{4}{9}\right)^{26}\)
\(b,\left(-\dfrac{1}{5}\right)^{10}:\left(\dfrac{1}{5}\right)^7\)
\(\left(-\dfrac{1}{5}\right)^{10}=\left(\dfrac{1}{5}\right)^{10}\) (vì có số mũ chẵn là `10`)
\(=\left(\dfrac{1}{5}\right)^{10}:\left(\dfrac{1}{5}\right)^7\)
\(=\left(\dfrac{1}{5}\right)^{10-7}=\left(\dfrac{1}{5}\right)^3=\dfrac{1}{125}\)
\(d,\left(\dfrac{2}{3}\right)^{18}:\left(\dfrac{12}{18}\right)^9\)
\(=\left(\dfrac{2}{3}\right)^{18}:\left(\dfrac{2}{3}\right)^9\)
\(=\left(\dfrac{2}{3}\right)^{18-9}\)
\(=\left(\dfrac{2}{3}\right)^9\)
Bài `3`
\(a,\dfrac{45^{10}\cdot5^{10}}{75^{10}}\)
\(=\dfrac{\left(45\cdot5\right)^{10}}{75^{10}}\)
\(=\dfrac{225^{10}}{75^{10}}\)\(=\left(225:75\right)^{10}=3^{10}\)
\(b,\dfrac{2^{17}\cdot9^4}{6^3\cdot8^3}\)
\(=\dfrac{2^{17}\cdot\left(3^2\right)^4}{\left(2\cdot3\right)^3\cdot\left(2^3\right)^3}\)
\(=\dfrac{2^{17}\cdot3^8}{2^3\cdot3^3\cdot2^9}=\dfrac{2^{17}\cdot3^8}{\left(2^3\cdot2^9\right)\cdot3^3}\)
\(=\dfrac{2^{17}\cdot3^8}{2^{12}\cdot3^3}=\dfrac{2^5\cdot3^5}{1\cdot1}=\left(2\cdot3\right)^5=6^5\)
\(c,\dfrac{8^2\cdot4^5}{2^{20}}\)
\(=\dfrac{\left(2^3\right)^2\cdot\left(2^2\right)^5}{2^{20}}=\dfrac{2^6\cdot2^{10}}{2^{20}}=\dfrac{2^{16}}{2^{20}}=\dfrac{1}{16}\)
\(d,\dfrac{4^5\cdot9^4}{8^3\cdot27^3}\)
\(=\dfrac{\left(2^2\right)^5\cdot\left(3^2\right)^4}{\left(2^3\right)^3\cdot\left(3^3\right)^3}\)
\(=\dfrac{2^{10}\cdot3^8}{2^9\cdot3^9}\)
\(=\dfrac{2\cdot1}{1\cdot3}=\dfrac{2}{3}\)
Công thức :
\(1,a^m\cdot a^n=a^{m+n}\)
\(2,a^m:a^n=a^{m-n}\)
\(3,\left(\dfrac{m}{n}\right)^a=\dfrac{m^a}{n^a}\)
\(4,a^m\cdot b^m=\left(a\cdot b\right)^m\)
\(5,a^m:b^m=\left(a:b\right)^m\)
các bạn giải giúp m với ạ! Mình đang cần gấp bài 2 và bài 3II
