a) \(27^7\div9^{10}\)

\(=\left(3^3\right)^7\div\left(3^2\right)^{10}\)

\(=3^{3\times7}\div3^{2\times10}\)

\(=3^{21}\div3^{20}\)

\(=3^1\)

\(=3\)

b) \(125^6\div25^7\)

\(=\left(5^3\right)^6\div\left(5^2\right)^7\)

\(=5^{3\times6}\div5^{2\times7}\)

\(=5^{18}\div5^{14}\)

\(=5^4\)

\(=625\)

c) \(5^{15}\div5^3\)

\(=5^{12}\)

\(=244140625\)

d) \(11^7\div11^3\)

\(=11^4\)

\(=14641\)

e) \(125\div5^2\)

\(=5^2\div5^2\)

\(=5^1\)

\(=5\)

g) \(169\div13^2\)

\(=13^2\div13^2\)

\(=13^1\)

\(=13\)

\(4^8.2^{20}=2^{16}.2^{20}=2^{36}\)

\(9^{12}.27^5.81^4=3^{24}.3^{15}.3^{16}=3^{55}\)

mk chỉnh đề

\(64^3.4^5.16^2=4^9.4^5.4^4=4^{18}\)

\(25^{20}.125^4=5^{40}.5^{12}=5^{52}\)

\(x^7.x^4.x^3=x^{14}\)

cái này dễ thế mà cũng phải hỏi à bạn

a) \(9^{20}=\left(3^2\right)^{20}=3^{40}\)

\(27^{13}=\left(3^3\right)^{13}=3^{39}\)

vi \(3^{39}< 3^{40}\) nen \(9^{20}>27^{13}\)

b) \(125^5=\left(5^3\right)^5=5^{15}\)

\(25^7=\left(5^2\right)^7=5^{14}\)

vi \(5^{15}>5^{14}\) nen \(125^5>27^7\)

bai 3:

   the h hinh lap phuong la:

\(5^3=125\left(m^3\right)\)

canh tang len 3 lan:   \(5.3=15\left(lan\right)\)

the h hinh lap phuong khi canh tang len 3 lan 

\(15^3=3375\left(m^3\right)\)

the h tang so lan la:    \(3375:125=27\left(lan\right)\)

   dap so:  \(27lan\)

Bài 2:

Bạn đưa về cùng cơ số rồi so sánh số mũ thôi!

Bài 3;

a) Thể tích hình lập phương là:

5 .5 . 5= 125 (m³)

  Bài 1:

2^\(x\) = 4

2\(^x\) = 2²

 \(x=2\)

Vậy \(x=2\)

Bài 2:

2\(^x\) = 8

2\(^x\) = 2³

\(x=3\)

Vậy \(x=3\)

a) \(9^{21}.9^{33}=9^{21+33}=9^{54}\)

b) \(19^{11}.19.19=19^{11+1+1}=19^{13}\)

c) \(25^2.5^2.125=5^4.5^2.5^3=5^{4+2+3}=5^9\)

d) \(t^{2021}.t^2.\left(t^2\right)^2=t^{2021}.t^2.t^4=t^{2021+2+4}=t^{2027}\)

e) \(123^{14}:123^{13}=123^{14-13}=123\)

f) \(64^2:8^3=\left(8^2\right)^2:8^3=8^4:8^3=8^{4-3}=8=2^3\)

g) \(6^{10}:6^3:36=6^{10}:6^3:6^2=6^{10-3-2}=6^5\)

h) \(m^{20}:m^{10}.m^{10}=m^{20-10+10}=m^{20}\)

oke

a, \(\frac{6^5\cdot27^2}{7^3\cdot9^5}=\frac{2^5\cdot3^5\cdot\left(3^3\right)^2}{7^3\cdot\left(3^2\right)^5}=\frac{2^5\cdot3^5\cdot3^6}{7^3\cdot3^{10}}=\frac{2^5\cdot3^{11}}{7^3\cdot3^{10}}=\frac{2^5\cdot3}{7^3}\)

b, \(\frac{12^7\cdot9^3}{8^5\cdot27^3}=\frac{3^7\cdot2^{12}\cdot3^6}{2^{15}\cdot3^9}=\frac{2^{12}\cdot3^{13}}{2^{15}\cdot3^9}=\frac{3^4}{2^3}\)

c, \(\frac{20^6\cdot8^2}{16^3\cdot25^3}=\frac{2^{12}\cdot5^6\cdot2^6}{2^{12}\cdot5^6}=2^6\)