Question

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

Answer 1

Câu 1:

a) 2²²⁵ và 3¹⁵⁰

         Ta có:2²²⁵=(2⁹)²⁵=512²⁵

                  3¹⁵⁰=(3⁶)²⁵=729²⁵

       Vì 512²⁵<729²⁵

                 Suy ra: 2²²⁵<3¹⁵⁰

Answer 2

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)\(\left(\frac{1}{3}\right)^3.\frac{1}{3}.9^2=\left(\frac{1}{3}\right)^4.\left(3^2\right)^2=3^4.\left(\frac{1}{3}\right)^4=3^4:3^4=1\)

 

Answer 3

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 \(\left(8^7-2^{18}\right)⋮14\)