Question

[deviated gamer]

rút gọn phân số 7*5^9*9^5/15^10

Answer 1

[Nguyễn Ngọc Hân]

7*5^9*9^5/15^10

=7*5^9*9^5/5^10*3^10

=7*9^5/5*3^10

=7*9^5/9^5

=7/5

k cho mik zới

Answer 2

[Hoang Khoi]

\(\frac{7\cdot5^9\cdot9^5}{15^{10}}=x\)

<=>\(7\cdot9^5=x\left(\frac{15^{10}}{5^9}\right)\)

<=>\(7\cdot9^5=x\left(\frac{3^{10}\cdot5^{10}}{5^9}\right)\)

<=>\(7\cdot9^5=x\left(3^{10}\cdot5\right)\)

<=>\(log_e\left(\frac{7}{5}\cdot9^5\right)=log_e\left(x\cdot3^{10}\right)\)

<=>\(log_e\left(\frac{7}{5}\right)+log_e\left(9^5\right)=log_e\left(x\right)+log_e\left(3^{10}\right)\)

<=>\(log_e\left(\frac{7}{5}\right)+log_e\left(3^{10}\right)=log_e\left(x\right)+log_e\left(3^{10}\right)\)

<=>\(log_e\left(\frac{7}{5}\right)=log_e\left(x\right)\)

<=>\(x=e^{ln\left(\frac{7}{5}\right)}\)

=>\(x=\frac{7}{5}\)