Question

Viết gọn !!
1, \(2^6.3^3.12^2\)

2, \(20^4:2^6\)

3, \(100^3:2^5\)

4, \(125^2.9^3.2^6\)

5, \(81^4.9^2.3^7\)

6, \(250^6:5^5\)

Answer 1

a)  \(2^6.3^3.12^2=2^{2.3}.3^3.12^2=4^3.3^3.12^2=12^3.12^2=12^5\)

b)  \(20^4:2^6=\left(2^2.5\right)^4:2^6=2^8.5^4:2^6=2^2.5^4=2^2.25^2=50^2\)

c) \(100^3:2^5=\left(25.2^2\right)^3:2^5=25^3.2^6:2^5=25^3.2\)

d) \(125^2.9^3.2^6=\left(5^3\right)^2.\left(3^2\right)^3.2^6=5^6.3^6.2^6=30^6\)

e) \(81^4.9^2.3^7= \left(3^4\right)^4.\left(3^2\right)^2.3^7=3^{16}.3^4.3^7=3^{27}\)

g) \(250^6:5^5=\left(2.5^3\right)^6:5^5=2^6.5^{18}:5^6=2^6.5^{12}=50^6\)

Answer 2

1,2⁶.3³.2⁴.3²=2¹⁰.3⁵

2,2⁸.5⁴:2⁶=2².5⁴

3,2².5²:2⁵=\(\frac{1}{2^3}.5^2\)

4,5⁶.9².2⁶=10⁶.9²

5,3¹⁶.3⁴.3⁷=3²⁷

6,5¹⁸.2:5⁵=5¹³.2

Answer 3

\(2^6\cdot3^3\cdot12^2=2^6\cdot3^3\cdot\left(3\cdot2^2\right)^2\)

                           \(=2^6\cdot3^3\cdot3^2\cdot2^4\)

                              \(=2^{10}\cdot3^5\)