a) 1⁵ + 2³ = 1 + 8 = 9 = 3² ( là số chính phương )

b) 5² + 12² = 25 + 144 = 169 = 13² ( là số chính phương )

c) 2⁶ + 6² = 64 + 36 = 100 = 100² ( là số chính phương )

d) 1³ + 2³ + 3³ + 4³ + 5³ + 6³

= 1 + 8 + 27 + 64 + 125 + 216

= 441 = 21² ( là số chính phương )

a) 1⁵ + 2³=1 + 8 = 9 (là số chính phương)

b) 5² + 12²= 25 + 144= 169 (là số chính phương)

c) 2⁶ + 6²= 64 + 36=100 (là số chính phương)

d) 14² – 12²= 196 - 144=52 (không là số chính phương)

e) 1³ + 2³ + 3³ + 4³ + 5³ + 6³= 1 + 8 + 27 + 64 + 125 + 216 = 411 (là số chính phương)

i) \(2345-1000\div\left[19-2\left(21-18\right)^2\right]\)

\(=\)\(2345-1000\div\left[19-2.3^2\right]\)

\(=\)\(2345-1000\div\left[19-2.9\right]\)

\(=\)\(2345-1000\div\left[19-18\right]\)

\(=\)\(2345-1000\div1\)

\(=\)\(2345-1000\)

\(=\)\(1345\)

j) \(128-\left[68+8\left(37-35\right)^2\right]\div4\)

\(=\)\(128-\left[68+8.2^2\right]\div4\)

\(=\)\(128-\left[68+8.4\right]\div4\)

\(=\)\(128-\left[68+32\right]\div4\)

\(=\)\(128-100\div4\)

\(=\)\(128-25\)

\(=\)\(3\)

k) \(568-\left\{5\left[143-\left(4-1\right)^2\right]+10\right\}\div10\)

\(=\)\(568-\left\{5\left[143-3^2\right]+10\right\}\div10\)

\(=\)\(568-\left\{5\left[143-9\right]+10\right\}\div10\)

\(=\)\(568-\left\{5.134+10\right\}\div10\)

\(=\)\(568-\left\{670+10\right\}\div10\)

\(=\)\(568-680\div10\)

\(=\)\(568-68\)

\(=\)\(500\)

a) \(107-\left\{38+\left[7.3^2-24\div6+\left(9-7\right)^3\right]\right\}\div15\)

\(=\)\(107-\left\{38+\left[7.3^2-24\div6+2^3\right]\right\}\div15\)

\(=\)\(107-\left\{38+\left[7.9-4+8\right]\right\}\div15\)

\(=\)\(107-\left\{38+\left[63-4+8\right]\right\}\div15\)

\(=\)\(107-\left\{38+67\right\}\div15\)

\(=\)\(107-105\div15\)

\(=\)\(107-7\)

\(=\)\(7\)

b) \(307-\left[\left(180-160\right)\div2^2+9\right]\div2\)

\(=\)\(307-\left[20\div4+9\right]\div2\)

\(=\)\(307-\left[5+9\right]\div2\)

\(=\)\(307-14\div2\)

\(=\)\(307-7\)

\(=\)\(300\)

c) \(205-\left[1200-\left(4^2-2.3\right)^3\right]\div40\)

\(=\)\(205-\left[1200-\left(16-6\right)^3\right]\div40\)

\(=\)\(205-\left[1200-10^3\right]\div40\)

\(=\)\(205-\left[1200-1000\right]\div40\)

\(=\)\(205-200\div40\)

\(=\)\(205-5\)

\(=\)\(200\)

Answer:

a) 

Có:

\(15=1.15=\left(-1\right).\left(-15\right)=3.5=\left(-3\right).\left(-5\right)\)

b) 

Có:

\(M=1+3+3^2+3^3+3^4+...+3^{98}+3^{99}+3^{100}\)

\(=\left(1+3\right)+\left(3^2+3^3+3^4\right)+...+\left(3^{98}+3^{99}+3^{100}\right)\)

\(=4+3^2.\left(1+3+3^2\right)+...+3^{98}.\left(1+3+3^2\right)\)

\(=4+3^2.13+3^{98}.13\)

\(=4+13.\left(3^2+...+3^{98}\right)\)

Vậy M chia 13 dư 4

Có:

\(M=1+3+3^2+3^3+3^4+...+3^{99}+3^{100}\)

\(=1+\left(3+3^2+3^3+3^4\right)+\left(3^5+3^6+3^7+3^8\right)+...+\left(3^{97}+3^{98}+3^{99}+3^{100}\right)\)

\(=1+3.40+3^5.40+...+3^{97}.40\)

\(=1+40.\left(3+3^5+...+3^{97}\right)⋮40\)

Mà \(40\left(3+3^5+...+3^{97}\right)⋮40\)

Vậy M chia 40 dư 1

\(5^{20}:\left(5^{15}.6+5^{15}.19\right)\)

\(=5^{20}:\left(5^{15}\left(6+19\right)\right)\)

\(=5^{20}:\left(5^{15}.25\right)\)

\(=5^{20}:\left(5^{15}.5^2\right)\)

\(=5^{20}:\left(5^{15+2}\right)\)

\(=5^{20}:5^{17}\)

\(=5^{20-17}\)

\(=5^3=125\)

a)  5²⁰ : (5¹⁵.6 + 5¹⁵.19)

= 5²⁰  : [ 5¹⁵ . ( 6 + 19 ) ]

= 5²⁰  : [ 5¹⁵ . 25 ]

=  5²⁰  : [ 5¹⁵ . 5² ]

=  5²⁰  : [ 5^{15 + 2} ]

=  5²⁰  : 5¹⁷

= 5^{20 - 17}

= 5³

^{= 125.}

^{Hok tốt !}

a t21B uhx53

Bài 2*: So sánh:

a)     A = 2⁰ +  2¹ + 2² + 2³ + … + 2²⁰¹⁰

2A = 2(1 + 2¹+ 2²+..+2²⁰¹⁰)

2A = 2¹+2²+2³+..+2²⁰¹¹

A = 2²⁰¹¹- 2⁰

A = 2²⁰¹¹-1

=> A = B

b) A = 2009 . 2011

A = 2009  (2010  + 1 )

A = 2009 . 2010+ 2009 . 1

A = 2010 . 2009 + 2009

B = 2010²

B = 2010. 2010

B = 2010 . (2009 + 1)

B = 2010 . 2009 + 2010 . 1

B = 2010 . 2009 + 2010

Ta thấy 2010 >  2009 nên 2010 . 2009 + 2010  > 2010 . 2009 + 2009

c) A = 10³⁰ = (10³)¹⁰ = 1000¹⁰

B = 2100 = (2¹⁰)¹⁰ = 1024¹⁰

=> A < B

d) A = 333⁴⁴⁴= (333⁴)¹¹¹ = (111⁴.81)¹¹¹

B = 444³³³= (444³)¹¹¹ = (111³.64)¹¹¹

=> A > B

e) A = 3⁴⁵⁰ = 3^3.150 = (3³)¹⁵⁰= 27¹⁵⁰

B = 5³⁰⁰ = 5^3.100= (5³)¹⁵⁰ = 15¹⁵⁰

=> A > B

*à xin lỗi cho mình sửa chỗ B câu cuối*

B  5⁴⁵⁰ = (5²)¹⁵⁰ = 25¹⁵⁰

=> A > B