Question

Bài 1: Rút gọn các biểu thức sau:

a) \(\frac{28^{15}.3^{17}}{84^{16}}\)                                                     b) \(\frac{3^{10}+6^2}{5.3^8+20}\)

Bài 2: So sánh

72^15 và 3^21.96^9

Answer 1

1:a)\(\frac{28^{15}\cdot3^{17}}{84^{16}}\)=\(\frac{28^{15}\cdot3^{15}\cdot3^2}{84^{16}}\)=\(\frac{\left(28^{15}\cdot3^{15}\right)\cdot3^2}{84^{16}}\)=\(\frac{84^{15}\cdot9}{84^{16}}\)=\(\frac{9}{84}\)=\(\frac{3}{28}\)

b)\(\frac{3^{10}+6^2}{5\cdot3^8+20}\)=\(\frac{3^2\cdot3^8+2^2\cdot3^2}{5\cdot3^8+5\cdot4}\)=\(\frac{9\cdot3^8+4\cdot9}{5\cdot\left(3^8+4\right)}\)=\(\frac{9\cdot\left(3^8+4\right)}{5\cdot\left(3^8+4\right)}\)=\(\frac{9}{5}\)

Answer 2

Xét vế trái ta có:72^15=3^15*24^15=3^15*24^9*24^6

=3^15*24^9*12^6*2^6=3^15*24^9*12^6*4^3(1)

Xét vế phải ta có: 3^21*96^9=3^15*3^6*24^9*4^9

=3^15*3^6*24^9*4^6*4^3=3^15*24^9*(3^6*4^6*4^3)

=3^15*24^9*(12^6*4^3)(2)

từ (1) và (2)=>72^15=3^21*96^9