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a) Ta có: \(\left(-2\right)^3+\frac{1}{2}:\frac{1}{8}-\sqrt{25}+\left|-64\right|\)
\(=-8+\frac{1}{2}\cdot8-5+64\)
\(=-8+4-5+64=55\)
b) Ta có: \(\left(\frac{-3}{4}+\frac{2}{7}\right):\frac{2}{3}+\left(\frac{-1}{4}+\frac{5}{7}\right):\frac{2}{3}\)
\(=\left(\frac{-3}{4}+\frac{2}{7}\right)\cdot\frac{3}{2}+\left(\frac{-1}{4}+\frac{5}{7}\right)\cdot\frac{3}{2}\)
\(=\left(\frac{-3}{4}+\frac{2}{7}+\frac{-1}{4}+\frac{5}{7}\right)\cdot\frac{3}{2}\)
\(=0\cdot\frac{3}{2}=0\)
c) Ta có: \(\frac{4^5\cdot9^4-2\cdot6^9}{2^{10}\cdot3^8+6^8\cdot20}\)
\(=\frac{2^{10}\cdot9^4-2\cdot6^9}{2^{10}\cdot3^8+2^8\cdot3^8\cdot20}=\frac{2\left(2^9\cdot9^4-6^9\right)}{6^8\left(2^2+20\right)}=\frac{-1}{3}\)
a) ( -2 )3 + \(\frac{1}{2}:\frac{1}{8}\) - √25 + \(|-64|\)
= \(\frac{-8}{1}\) + \(\frac{1}{2}.\frac{8}{1}\) - \(\frac{5}{1}\) + \(\frac{64}{1}\)
= \(\frac{-16}{2}+\frac{1}{2}.\frac{8}{1}-\frac{10}{2}+\frac{128}{2}\)
= \(\frac{-16}{2}+\frac{8}{2}-\frac{10}{2}+\frac{128}{2}\)
= \(\frac{-16+8-10+128}{2}\) = \(\frac{110}{2}\) = 55
Giải:
Đặt \(\frac{a}{b}=\frac{c}{d}=k\)
\(\Rightarrow a=bk,c=dk\)
Ta có: \(\frac{a.b}{c.d}=\frac{bkb}{dkd}=\frac{b^2}{d^2}\) (1)
\(\frac{\left(a+b\right)^2}{\left(c+d\right)^2}=\frac{\left(bk+b\right)^2}{\left(dk+d\right)^2}=\frac{\left[b\left(k+1\right)\right]^2}{\left[d\left(k+1\right)\right]^2}=\frac{b^2}{d^2}\) (2)
\(\frac{a^2+b^2}{c^2+d^2}=\frac{\left(bk\right)^2+b^2}{\left(dk\right)^2+d^2}=\frac{b^2.k^2+b^2}{d^2.k^2+d^2}=\frac{b^2.\left(k^2+1\right)}{d^2.\left(k^2+1\right)}=\frac{b^2}{d^2}\) (3)
Từ (1), (2) và (3) suy ra \(\frac{a.b}{c.d}=\frac{\left(a+b\right)^2}{\left(c+d\right)^2}=\frac{a^2+b^2}{c^2+d^2}\)
Đặt \(\frac{a}{b}=\frac{c}{d}=k\Rightarrow\begin{cases}a=bk\\c=dk\end{cases}\)
ta có: \(\frac{a.b}{c.d}=\frac{b^2.k}{d^2.k}=\frac{b^2}{d^2}\left(1\right)\)
\(\frac{\left(a+b\right)^2}{\left(c+d\right)^2}=\frac{a^2+2ab+b^2}{c^2+2cd+d^2}=\frac{b^2.k^2+2b^2.k+b^2}{d^2.k^2+2d^2.k+d^2}=\frac{b^2}{d^2}\left(2\right)\)
\(\frac{a^2+b^2}{c^2+d^2}=\frac{b^2.k^2+b^2}{d^2.k^2+d^2}=\frac{b^2}{d^2}\left(3\right)\)
từ 1,2 và 3 ta có điều phải chứng minh
a) \(\frac{45^{10}.5^{20}}{75^{15}}\)
=
\(\frac{\left(5.9\right)^{10}.5^{20}}{\left(5.15\right)^{15}}\)
= \(\frac{5^{10}.9^{10}.5^{20}}{5^{15}.15^{15}}\)
= \(\frac{5^{10}.3^{20}.5^{20}}{5^{15}.15^{15}}\)
= \(\frac{5^{10}.15^{20}}{5^{15}.15^{15}}\)
= \(\frac{15^5}{5^5}\)
= \(\frac{3^5.5^5}{5^5}\)
= \(3^5\)
b) \(\frac{\left(0,8\right)^5}{\left(0,4\right)^6}\)
= \(\frac{\left(0,4\right)^5.2^5}{\left(0,4\right)^6}\)
= \(\frac{2^5}{0,4}\)
= \(2^5\) : 0,4
(=) 32 : \(\frac{2}{5}\)
= 90
c) \(\frac{2^{15}.9^4}{6^6.8^3}\)
= \(\frac{2^{15}.\left(3^2\right)^4}{\left(2.3\right)^6.\left(2^3\right)^3}\)
= \(\frac{2^{15}.3^8}{2^6.3^6.2^9}\)
= \(3^2\)
a) \(-\frac{48}{625}\)
b) không có giá trị
c) 1:125
d) \(-\frac{1053}{500}\)
e) 1
g) -13
a) \(-\dfrac{48}{625}\)
b) \(\varnothing\)
c) \(\dfrac{1}{125}\)
d) \(-\dfrac{1053}{500}\)
e) 1
f) -13