\(\frac{9^{14}.25^5.8^7}{18^{12}.625^3.24^3}\)

\(=\frac{\left(3^2\right)^{14}.\left(5^2\right)^5.\left(2^3\right)^7}{\left(2.3^2\right)^{12}.\left(5^4\right)^3.\left(2^3.3\right)^3}\)

\(=\frac{3^{28}.5^{10}.2^{21}}{2^{12}.3^{24}.5^{12}.2^9.3}\)

\(=\frac{3^{28}.5^{10}.2^{21}}{2^{21}.3^{25}.5^{12}}\)

\(=\frac{3^3.1.1}{1.1.5^2}\)

\(=\frac{27}{25}\)

Sai rồi

Ta có: \(\dfrac{9^{14}.25^5.8^7}{18^{12}.625^3.24^3}\)= \(\dfrac{9^{14}.25^5.8^7}{9^{12}.2^{12}.\left(25^2\right)^3.8^3.3^3}\)=\(\dfrac{9^{12}.9^2.25^5.8^7}{9^{12}.2^{12}.25^6.8^3.3^3}\)

= \(\dfrac{9^{12}.3^4.25^5.8^7}{9^{12}.\left(2^{12}.8^3\right).25^5.25.3^3}\)=\(\dfrac{9^{12}.3^3.3.25^5.8^7}{9^{12}.8^7.25^5.25.3^3}\)=\(\dfrac{\left(9^{12}.3^3.25^5.8^7\right).3}{\left(9^{12}.3^3.25^5.8^7\right).25}\)

=\(\dfrac{3}{25}\)

( Có một vài bước mik làm tắt bặn nhé!)

\(\frac{9^{14}\cdot25^5\cdot8^7}{18^{12}\cdot625^3\cdot24^3}=\frac{\left(3^2\right)^{14}\cdot\left(5^2\right)^5\cdot\left(2^3\right)^7}{\left(3^2\cdot2\right)^{12}\cdot\left(5^4\right)^3\cdot\left(3\cdot2^3\right)^3}\)

\(=\frac{3^{28}\cdot5^{10}\cdot2^{21}}{3^{24}\cdot2^{12}\cdot5^{12}\cdot3^3\cdot2^9}=\frac{3^{28}\cdot5^{10}\cdot2^{21}}{3^{25}\cdot5^{12}\cdot2^{21}}=\frac{3^3}{5^2}=\frac{27}{25}\)

a,999/2610=111/290

b,374/506=17/23

c,3600-75/8400-175=3/7

d,9^14.25^5.8^7/18^12.625^3.24^3=3/25

a, Ta có:999/2610=111/290

b, Ta có:374/506=17/2

c,Ta có:3600-75/8400-175=48.75-75/48.175-175=75.(48-1)/175.(48-1)=75/175=3/7

d, Ta có:(3^2)^14.(5^2)^5.(2^3)^7/(2.3^2)^12.(5^4)^3.(2^3.3)^3

=3^28.5^10.2^21/2^12.3^24.5^12.2^9.3^3

=3^28.5^10.2^21/2^21.3^27.5^12

=3/5^2=3/25

\(\frac{9^9\cdot225^5\cdot8^7}{18^{12}\cdot625^3\cdot24^3}=\frac{9^9\cdot\left(\left(3\cdot5\right)^2\right)^5\cdot8^7}{\left(9\cdot2\right)^{12}\cdot\left(\left(5^2\right)^2\right)^3\cdot\left(8\cdot3\right)^3}\)

\(=\frac{1}{9^3\cdot2^{12}}\cdot\frac{9^5\cdot5^{10}}{5^{12}}\cdot\frac{8^7}{8^3\cdot3^3}\)

\(=\frac{9^2\cdot8^4}{2^{12}\cdot5^2\cdot3^3}\)

\(=\frac{9\cdot\left(2^4\right)^3}{\left(2^4\right)^3\cdot5^2}\)

\(=\frac{9}{25}\)

\(\dfrac{9^{14}.25^6.8^7}{18^{12}.625^3.24^3}=\dfrac{\left(3^2\right)^{14}.\left(5^2\right)^6.\left(2^3\right)^7}{\left(2.3^2\right)^{12}.\left(5^4\right)^3.\left(2^3.3\right)^3}\)

\(=\dfrac{3^{28}.5^{12}.2^{21}}{2^{21}.3^{27}.5^{12}}=\dfrac{3}{1}=3\)

\(A=\dfrac{9^{14}.25^6.8^7}{18^{12}.625^3.24^3}=\dfrac{\left(3^2\right)^{14}.\left(5^2\right)^6.\left(2^3\right)^7}{\left(2.3^2\right)^{12}.\left(5^4\right)^3.\left(3.2^3\right)^3}\)

=\(\dfrac{3^{28}.5^{12}.2^{21}}{2^{12}.3^{24}.5^{12}.3^3.2^9}\)=\(\dfrac{3^{28}.5^{12}.2^{21}}{2^{21}.3^{27}.5^{12}}=3\)

\(\frac{9^{14}}{18^{12}}.\frac{25^5}{625^3}.\frac{8^7}{24^3}\)

\(=\frac{9^{14}}{\left(9.2\right)^{12}}.\frac{25^5}{25^6}.\frac{8^7}{\left(8.3\right)^3}\)

\(=\frac{9^{14}}{9^{12}.2^{12}}.\frac{1}{25}.\frac{8^7}{8^3.3^3}\)

\(=\frac{9^2}{2^{12}}.\frac{1}{25}.\frac{8^4}{3^3}\)

\(=\frac{81}{4096}.\frac{1}{25}.\frac{4096}{27}\)

\(=\frac{81}{4096}.\frac{4096}{27}.\frac{1}{24}=3.\frac{1}{24}=\frac{3}{24}\)

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