c) 7³ : 7 - 4⁵ : 4³

= 7² - 4²

= 49 - 16

= 33

d) 8⁷ : 8⁴ : 8² + 8

= 8 + 8

= 16

a) 6³ : 6² + 94

= 6 + 94

= 100

b) 135 - 5⁴ : 5²

= 135 - 5²

= 135 - 25

= 110

\(a,6^3:6^2+94=6+94=100\\ b,135-5^4:5^2=135-5^2=110\\ c,7^3:7-4^5:4^3=7^2-4^2=33\\ d,8^7:8^4:8^2+8=8+8=16\)

a,6³:6²+94=6+94=100

b,135-5⁴:5²=135-5²=135-25=110

c,7³:7-4⁵:4³=7²-4²=49-16=33

d,8⁷:8⁴:8²+8=8+8=16.

\(a,6^3:6^2+94=6+94=100\\ b,135-5^4:5^2=135-5^2=135-25=110\\ c,7^3:7-4^5:4^3=7^2-4^2=49-16=33\\ d,8^7:8^4:8^2+8=8^2+8=64+8=72\)

a, 2¹.5².17 = 2.25.17 = 50.17 = 850 

b, 2² + 2³ + 2⁴ = 4 + 8 + 16 = 28

c, 2⁵.3 + 2⁴:8 + 50: 5²

= 32.3 + 16:8 + 50:25

=96 + 2 + 2

= 100

d, 11² - 10² - 3²

= 121 - 100 - 9

= 21 - 9

= 12

e, 1³ + 2³ + 3³ + 4³ + 5³

= ( 1+ 2+3+4+5)²

= 15²

= 225

1)Tính:

a)\(4^2\cdot2=\left(2^2\right)^2\cdot2=2^4\cdot2=2^5=32\)

b)\(36^2:6^2=\left(36:6\right)^2=6^2=48\)

c)\(\left(\frac{2}{5}\right)^{10}:\left(\frac{4}{25}\right)^2=\left(\frac{2}{5}\right)^{10}\cdot\left(\frac{25}{4}\right)^2=\)\(\left(1\right)^{10}\cdot\left(\frac{5}{2}\right)^2=1\cdot\frac{5^2}{2^2}=1\cdot\frac{25}{4}=\frac{25}{4}\)

a

\(4^2.2=16.2=32\)

b\(36^2:6^2=36.36:6.6=36.36:36=36\)

c

a) Ta có : A=2+2²+2³+...+2¹⁰

                  =(2+2²)+(2³+2⁴)+...+(2⁹+2¹⁰)

                 =2(1+2)+2³(1+2)+...+2⁹(1+2)

                =2.3+2³.3+...+2⁹.3

Vì 3\(⋮\)3 nên 2.3+2³.3+...+2⁹.3\(⋮\)3

hay A\(⋮\)3

Vậy A\(⋮\)3.

b) Ta có : A=2²+2⁴+2⁶+...+2²⁰

                  =(2²+2⁴)+(2⁶+2⁷)+...+(2¹⁸+2²⁰)

                  =2²(1+2²)+2⁶(1+2²)+...+2¹⁸(1+2²)

                 =2².5+2⁶.5+...+2¹⁸.5

Vì 5\(⋮\)5 nên 2².5+2⁶.5+...+2¹⁸.5\(⋮\)5

hay A\(⋮\)5

Vậy A\(⋮\)5.

Ta có :

4 mũ 3=4.4.4=64;8 mũ 2=8.8=64

Bởi vì 64=64 nên suy ra 4 mũ 3= 8 mũ 2

\(A=5+5^2+5^3+5^4+...+5^{39}+5^{40}\)

\(=\left(5+5^2\right)+\left(5^3+5^4\right)+...+\left(5^{39}+5^{40}\right)\)

\(=5\left(1+5\right)+5^3\left(1+5\right)+...+5^{39}\left(1+5\right)\)

\(=6\left(5+5^3+...+5^{39}\right)⋮6\)

Suy ra \(A⋮3,A⋮2\).

5+5²+5³+.....+5²⁹+5³⁰

= (5+5²)+ (5³+5⁴)+.............+(5²⁹+5³⁰)

= 5(1+5) + 5³(1+5)+....+5²⁹(1+5)

= 5.6 + 5³.6 +....+5²⁹.6

= 6( 5+5³+....+5²⁹)

Vì 6 \(⋮\)6 nên 6( 5+5³+....+5²⁹)\(⋮\)6

Vậy.....