1. So sánh :
a) 2225 và 3150
b) 291 và 535
2. Tính:
a) 253 : 52
b) (3/7)21 : (9/49)6
c) 3 - (-6/7)0 + (1/2)2 : 2
3. Viết các biểu thức số sau dưới dạng an (a thuộc Q, n thuộc N)
a) 9 . 33 . 1/81 . 32
b) 4 . 25 : (23 .1/16)
c) 32 . 25 .(2/3)2
d) (1/3)2 . 1/3 .92
4. Chứng minh rằng: 87- 218 chia hết cho 14
Giúp mik vs, thanks trc nha
Câu 1:
a) 2225 và 3150
Ta có:2225=(29)25=51225
3150=(36)25=72925
Vì 51225<72925
Suy ra: 2225<3150
Câu 2:
a)\(25^3:5^2=\left(5^2\right)^3:5^2=5^6:5^2=5^4\)
b)\(\left(\frac{3}{7}\right)^{21}:\left(\frac{9}{49}\right)^6=\left(\frac{3}{7}\right)^{21}:\left[\left(\frac{3}{7}\right)^2\right]^6=\left(\frac{3}{7}\right)^{21}:\left(\frac{3}{7}\right)^{12}=\left(\frac{3}{7}\right)^9\)
c)\(3-\left(-\frac{6}{7}\right)^0+\left(\frac{1}{2}\right)^2:2=3+\frac{1}{4}:2=3+\frac{1}{8}=\frac{25}{8}\)
Câu 3:
a)\(9.3^3.\frac{1}{81}.3^2=3^2.3^3.3^2.\left(\frac{1}{3^4}\right)=3^7:3^4=3^3\)
b)\(4.2^5:\left(2^3.\frac{1}{16}\right)=2^2.2^5:\left(2^3.\frac{1}{2^4}\right)=2^7:\frac{1}{2}=2^8\)
c)\(3^2.2^5.\left(\frac{2}{3}\right)^2=288.\frac{4}{9}=2^7\)
d)\(\left(\frac{1}{3}\right)^3.\frac{1}{3}.9^2=\left(\frac{1}{3}\right)^4.\left(3^2\right)^2=3^4.\left(\frac{1}{3}\right)^4=3^4:3^4=1\)
Câu 4:
Ta có: \(8^7-2^{18}\)
\(=\left(2^3\right)^7-2^{18}\)
\(=2^{21}-2^{18}\)
\(=2^{17+4}-2^{17+1}\)
\(=2^{17}.2^4-2^{17}.2\)
\(=2^{17}\left(2^4-2\right)\)
\(=2^{17}.14⋮14\)
Vậy \(\left(8^7-2^{18}\right)⋮14\)
