`a, = 5^3 xx 3^3 = 15^3`

`b, = 12^3 xx 4^3 = 48^3`

`c, = 625^3 xx 8^3 = 5000^3`

`d, = 625 ^3 xx 125^3 = 78125^3`

`e, = 5^20 : 5^14 = 5^6`

1,\(125\cdot27=5^3\cdot3^3=\left(5\cdot3\right)^3=15^3\)

2, \(12^3\cdot64=12^3\cdot4^3=\left(12\cdot4\right)^3=48^3\)

3, \(25^6\cdot8^3=\left(5^2\right)^6\cdot\left(2^3\right)^3=5^8\cdot2^9\)

4, \(25^6\cdot125^3=\left(5^2\right)^3\cdot\left(5^3\right)^3=5^6\cdot5^9=5^{15}\)

5,\(625^5:25^7=\left(5^4\right)^5:\left(5^2\right)^7=5^{20}:5^{14}=5^6\)

b: \(3^4\cdot3^5:\dfrac{1}{27}==3^9\cdot3^3=3^{12}\)

a: \(2^6\cdot3^3=\left(2^2\cdot3\right)^3=12^3\)

b: \(6^4\cdot8^3=2^4\cdot3^4\cdot2^9=2^{13}\cdot3^4\)

c: \(16\cdot81=36^2\)

d: \(25^4\cdot2^8=100^4\)

Bài 6: 

a: \(2^{27}=8^9\)

\(3^{18}=9^9\)

b: Vì \(8^9< 9^9\)

nên \(2^{27}< 3^{18}\)

a) 4¹⁶

b) 60¹⁵

c) x⁵⁰⁵⁰

a,4^16

60^15

x^5050

tich cho minh 

pheaeeeeeeeeeeeeeeeeeeeeeeeeeeee

a) \(\dfrac{9}{4}-3y+y^2\)

\(=\left(\dfrac{3}{2}\right)^2-3y+y^2\)

\(=y^2-2\cdot\dfrac{3}{2}\cdot y+\left(\dfrac{3}{2}\right)^2\)

\(=\left(y-\dfrac{3}{2}\right)^2\)

b) \(x^3+6x^2y+12xy^2+8y^3\)

\(=x^3+6x^2y+12xy^2+\left(2y\right)^3\)

\(=x^3+3\cdot x^2\cdot2y+3\cdot x\cdot\left(2y\right)^2+\left(2y\right)^3\)

\(=\left(x+2y\right)^2\)

\(\begin{array}{l}a){15^8}{.2^4} = {15^{2.4}}{.2^4} = {({15^2})^4}{.2^4}\\ = {225^4}{.2^4} = {(225.2)^4} = {450^4}\\b){27^5}:{32^3} = {({3^3})^5}:{({2^5})^3}\\ = {3^{3.5}}:{2^{5.3}} = {3^{15}}:{2^{15}} = {\left( {\frac{3}{2}} \right)^{15}}\end{array}\)

a) \(15^8\cdot2^4=3^8\cdot5^8\cdot2^4=9^4\cdot25^4\cdot2^4=\left(9\cdot25\cdot2\right)^4=450^4\) 

b) \(27^5:32^3=\left(3^3\right)^5:\left(2^5\right)^3=3^{15}:2^{15}=\left(\dfrac{3}{2}\right)^{15}\)

a, 4⁸.8⁴

= (2²)⁸.(2³)⁴

= 2¹⁶.2¹²

= 2²⁸

b, 4¹⁵.5¹⁵

= (4.5)¹⁵

= 20¹⁵

c, 2¹⁰.15 + 2¹⁰.85

= 2¹⁰.(15 + 85)

= 2¹⁰.100

=2¹⁰.(2.5)²

= 2¹².5²

d, 3³.9²

= 3³ . (3²)²

= 3³.3⁴

= 3⁷

e, 5¹².7 - 5¹¹.10

= 5¹¹.(5.7 - 10)

= 5¹¹.25

=5¹¹.5²

=5¹³

f, \(x^1\).\(x^2\).\(x^3\)....\(x^{100}\)

= \(x^{1+2+3+...+100}\)

= \(x^{\left(1+100\right).100:2}\)

= \(x^{5050}\)

❤Em cảm ơn cô Nguyễn Thương hoài rất nhiều a!❤

a, 48.84

= (22)8.(23)4

= 216.212

= 228

b, 415.515

= (4.5)15

= 2015

c, 210.15 + 210.85

= 210.(15 + 85)

= 210.100

=210.(2.5)2

= 212.52

d, 33.92

= 33 . (32)2

= 33.34

= 37

e, 512.7 - 511.10

= 511.(5.7 - 10)

= 511.25

=511.52

=513

f, �1x1.�2x2.�3x3....�100x100

= �1+2+3+...+100x1+2+3+...+100

= �(1+100).100:2x(1+100).100:2

= �5050x5050