a) \(\frac{125^{100}.2^{160}}{5^{289}.4^{80}}=\frac{\left(5^3\right)^{100}.2^{160}}{5^{289}.\left(2^2\right)^{80}}=\frac{5^{300}.2^{160}}{5^{289}.2^{160}}=5^{300-289}=5^{11}\)

b) \(\frac{9^8.8^8}{3^8.27^3.2^{24}}=\frac{\left(3^2\right)^8.\left(2^3\right)^8}{3^8.\left(3^3\right)^3.2^{24}}=\frac{3^{16}.2^{24}}{3^8.3^9.2^{24}}=\frac{3^{16}}{3^{17}}=\frac{1}{3}\)

a) \(\frac{125^{100}.2^{160}}{5^{289}.4^{80}}=\frac{\left(5^3\right)^{100}.2^{160}}{5^{289}.\left(2^2\right)^{80}}=\frac{5^{300}.2^{160}}{5^{289}.2^{160}}=5\)

b) \(\frac{9^8.8^8}{3^8.27^3.2^{24}}=\frac{\left(3^2\right)^8.\left(2^3\right)^8}{3^8.\left(3^3\right)^3.2^{24}}=\frac{3^{16}.2^{24}}{3^8.3^9.2^{24}}=\frac{3^{16}.2^{24}}{3^{17}.2^{24}}=\frac{1}{3}\)

a) \(\frac{125^{100}.2^{160}}{5^{289}.4^{80}}=\frac{\left(5^3\right)^{100}.2^{160}}{5^{289}.\left(2^2\right)^{80}}\)

                               \(=\frac{5^{300}.2^{160}}{5^{289}.2^{160}}=5^{11}=48828125\)

b) \(\frac{9^8.8^8}{3^8.27^3.2^{24}}=\frac{\left(3^2\right)^8.\left(2^3\right)^8}{3^8.\left(3^3\right)^3.2^{24}}\)

                            \(=\frac{3^{16}.2^{24}}{3^{17}.2^{24}}=3^{-1}=\frac{1}{3}\)

Chúc em học tốt nhé

a: \(=\dfrac{5^{300}\cdot2^{160}}{5^{289}\cdot2^{160}}=5^{11}\)

b: \(=\dfrac{250}{175-50-85+2\cdot5}=\dfrac{250}{125-85+10}=\dfrac{250}{50}=5\)

a) \(\left(\frac{3}{4}\right)^{45}:\left(\frac{9}{6}\right)^{10}\)

\(=\left(\frac{3}{4}\right)^{45}:\left(\frac{3}{4}\right)^{20}\)

\(=\left(\frac{3}{4}\right)^{25}\)

b) \(\frac{125^{100}.2^{160}}{5^{298}.4^{80}}\)

\(=\frac{5^{300}.2^{160}}{5^{298}.2^{160}}\)

\(=5^2=25\)

a) \(\left(\frac{3}{4}\right)^{45}:\left(\frac{9}{6}\right)^{10}\)

\(\Leftrightarrow\frac{\left(\frac{3}{4}\right)^{45}}{\frac{3^{10}}{2^{10}}}=\frac{\frac{3^{45}}{4^{45}}}{\frac{3^{10}}{2^{10}}}=\frac{3^{45}.2^{10}}{4^{45}}=\frac{3^{35}.2^{10}}{2^{90}}=\frac{3^{35}}{2^{80}}\)

\(\Rightarrow\left(\frac{3}{4}\right)^{45}:\left(\frac{9}{6}\right)^{10}=\frac{3^{35}}{2^{80}}\)

125¹⁰⁰.2¹⁶⁰/5²⁹⁸.4⁸⁰

=5³⁰⁰.2¹⁶⁰/5²⁹⁸.2¹⁶⁰

=5²=25

k mik nha

sao k ai trả lời

Bn đăng vào toán thì các CTV chuyên toán sẽ giúp bạn

\(\left(1+\dfrac{100}{20}\right)\) x \(\dfrac{125}{60}\)

\(=6\) x \(\dfrac{125}{60}\)

\(=\dfrac{750}{60}=\dfrac{25}{2}\)

\(=\left(\dfrac{1}{14^{100}}\cdot2^{160}\right):\left(5^{289}\cdot2^{160}\right)\)

\(=\dfrac{2^{160}}{2^{100}\cdot7^{100}}\cdot\dfrac{1}{5^{289}\cdot2^{160}}=\dfrac{1}{14^{100}\cdot5^{289}}\)

\(\left(125^{100}.2^{160}\right):\left(5^{289}.4^{80}\right)\)

\(\left(125^{100}.2^{160}\right):\left(5^{289}.4^{80}\right)\)\(=\frac{\left(5^3\right)^{100}.2^{100}}{5^{289}.\left(2^2\right)^{80}}\)\(=\frac{5^{300}.2^{100}}{5^{289}.2^{160}}\)\(=\frac{5^{11}}{2^{60}}\)

\(\left(9^8.5^8\right):\left(3^7.27^3.5^4\right)\)\(=\frac{\left(3^2\right)^8.5^8}{3^7.\left(3^3\right)^3.5^4}=\frac{3^{16}.5^4}{3^7.3^9}=\frac{3^{16}.5^4}{3^{16}}=5^4=625\)

\(\left(1024.27^8\right):\left(2^9.3^{23}\right)=\frac{2^{10}.\left(3^3\right)^8}{2^9.3^{23}}=\frac{2.3^{24}}{3^{23}}=2.3=6\)

\(\left(625.2^7+25^2.64\right):\left(2^6.5^4.3\right)=\frac{25^2.128+25^2.64}{2^6.\left(5^2\right)^2.3}=\frac{25^2.\left(128+64\right)}{64.25^2.3}=\frac{192}{192}=1\)

1, 3^4

2, 5^405

3, -20/3

4, 4

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