Ta có: \(30\cdot10^8\cdot5^4-25^6\cdot16^2\cdot3\)

\(=2\cdot3\cdot5\cdot2^8\cdot5^8\cdot5^4-5^{12}\cdot2^8\cdot3\)

\(=2^9\cdot3\cdot5^{13}-2^8\cdot3\cdot5^{12}=2^8\cdot3\cdot5^{12}\left(2\cdot5-1\right)=2^8\cdot3^3\cdot5^{12}\)

\(75^3\cdot20^4+3^3\cdot5^{10}\cdot32^2\)

\(=\left(5^2\cdot3\right)^3\cdot\left(2^2\cdot5\right)^4+3^3\cdot5^{10}\cdot2^{10}\)

\(=5^6\cdot3^3\cdot2^8\cdot5^4+3^3\cdot5^{10}\cdot2^{10}=3^3\cdot2^8\cdot5^{10}\left(1+5^2\right)=3^3\cdot2^9\cdot5^{10}\cdot13\)

Ta có: \(\frac{30\cdot10^8\cdot5^4-25^6\cdot16^2\cdot3}{75^3\cdot20^4+3^3\cdot5^{10}\cdot32^2}\)

\(=\frac{2^8\cdot3^3\cdot5^{12}}{3^3\cdot2^9\cdot5^{10}\cdot13}=\frac12\cdot\frac{5^2}{13}=\frac12\cdot\frac{25}{13}=\frac{25}{26}\)

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

Tử số :     \(4^5.9^4-2.6^9\)

        \(=\left(2^2\right)^5.\left(3^2\right)^4-2.2^9.3^9\)

        \(=2^{10}.3^8-2^{10}.3^9\)

Mẫu số :      \(2^{10}.3^8+6^8.20\)

           \(=2^{10}.3^8+2^8.3^8.2^2.5\)

           \(=2^{10}.3^8+2^{10}.3^8.5\)

             \(=2^{10}.3^8.6\) 

Trl

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