Question

[thanhan9825]

Rút gọn phân số sau :

\(\frac{9^{14}\times25^5\times8^7}{18^{12}\times625^3\times24^3}\)

làm giúp mình nha,mình đang cần gấp để mai nộp bài cho cô giáo

Answer 1

[Nguyễn Thị Thương Hoài]

A = \(\frac{9^{14}\times25^5\times8^7}{18^{12}\times625^2\times24^3}\)

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

A = \(\frac{3^{28}\times5^{10}\times2^{21}}{2^{12}\times3^{24}\times5^{12}\times2^9\times3^3}\)

A = \(\frac{3^{28}\times5^{10}\times2^{21}}{\left(3^{24}.3^3\right)\times5^{12}\times\left(2^{12}\times2^9\right)}\)

A = \(\frac{3^{28}\times5^{10}\times2^{21}}{3^{27}\times5^{12}\times2^{21}}\)

A = \(\frac{3}{5^2}\)

A = \(\frac{3}{25}\)

Answer 2

[Nguyễn Lê Phước Thịnh]

\(\dfrac{9^{14}\cdot25^5\cdot8^7}{18^{12}\cdot625^3\cdot24^3}\)

\(=\dfrac{3^{28}\cdot5^{10}\cdot2^{21}}{\left(2\cdot3^2\right)^{12}\cdot\left(5^4\right)^3\cdot\left(2^3\cdot3\right)^3}\)

\(=\dfrac{2^{21}\cdot3^{28}\cdot5^{10}}{2^{12}\cdot3^{24}\cdot5^{12}\cdot2^9\cdot3^3}\)

\(=\dfrac{2^{21}}{2^{21}}\cdot\dfrac{3^{28}}{3^{27}}\cdot\dfrac{5^{10}}{5^{12}}=\dfrac{3}{5^2}=\dfrac{3}{25}\)