d: =5^10*5^4/5^12=5^2

e: \(=\dfrac{2^{19}\cdot3^9+3^9\cdot2^{18}\cdot5}{2^{19}\cdot3^9+3^{10}\cdot2^{20}}\)

\(=\dfrac{2^{18}\cdot3^9\left(2+5\right)}{2^{19}\cdot3^9\left(1+3\cdot2\right)}=\dfrac{1}{2}\)

`@` `\text {Ans}`

`\downarrow`

`d)`

\(\dfrac{5^{10}\cdot25^2}{125^4}\)

`=`\(\dfrac{5^{10}\cdot\left(5^2\right)^2}{\left(5^3\right)^4}=\dfrac{5^{10}\cdot5^4}{5^{12}}=\dfrac{5^{14}}{5^{12}}=5^2\)

`e)`

\(\dfrac{2^{19}\cdot27^3+15\cdot4^9\cdot9^4}{6^9\cdot2^{10}+12^{10}}\)

`=`\(\dfrac{2^{19}\cdot3^9+3\cdot5\cdot2^{18}\cdot3^8}{2^9\cdot3^9\cdot2^{10}+2^{20}\cdot3^{10}}\)

`=`\(\dfrac{2^{19}\cdot3^9+5\cdot2^{18}\cdot3^9}{2^{19}\cdot3^9+2^{20}\cdot3^{10}}\)

`=`\(\dfrac{2^{18}\cdot3^9\left(2+5\right)}{2^{19}\cdot3^9\left(1+2\cdot3\right)}\)

`=`\(\dfrac{2^{18}\cdot3^9}{2^{19}\cdot3^9}=\dfrac{1}{2}\)

a: \(3\cdot3\cdot3\cdot3\cdot3=3^5\)

b: \(y\cdot y\cdot y\cdot y=y^4\)

c: \(5\cdot p\cdot5\cdot p\cdot2\cdot q\cdot4\cdot q=25\cdot2\cdot4\cdot p^2q^2=2\cdot\left(10qp\right)^2\)

d: \(a\cdot a+b\cdot b+c\cdot c+d\cdot d\cdot d\cdot d=a^2+b^2+c^2+d^4\)

a) 3.3.3.3.3 = 3\(^5\)

b) y.y.y.y = y\(^4\)

c) 5.p.5.p.2.q.4.q = 5\(^2\).p\(^2\).q\(^2\).2\(^3\) 

(2\(^3\) ở đây là vì 2.4 = 2.2.2 = 2\(^3\))

d) a.a + b.b + c.c.c + d.d.d.d = a\(^2\)+b\(^2\)+c\(^3\)+d\(^4\)

\(a,5\cdot p\cdot5\cdot p\cdot2q\cdot4q\)

\(=5^2\cdot p^2\cdot2\cdot q\cdot2^2\cdot q\)

\(=5^2\cdot2^3\cdot p^2\cdot q^2\)

\(b,a\cdot a+b\cdot b+c\cdot c\cdot c+d\cdot d\cdot d\cdot d\)

\(=a^2+b^2+c^3+d^4\)

#Urushi

100⁴.10⁹.10000⁵.1000⁷

= (10²)⁴.(10¹)⁹.(10⁴)⁵.(10³)⁷

= 10⁸.10⁹.10²⁰.10²¹

= 10^8+9+20+21

= 10⁵⁸

100⁴.10⁹.10000⁵.1000⁷

=(10²)⁴.10⁹.(10⁴)⁵.(10³)⁷

=10⁸.10⁹.10²⁰.10²¹

=10⁵⁸

\(100^4.10^9.10000^5.1000^7=\left(10^2\right)^4.10^9.\left(10^4\right)^5.\left(10^3\right)^7\)

\(=10^8.10^9.10^{20}.10^{21}=10^{8+9+20+21}=10^{58}\)

1.
a) \(3^4\times3^5\times3^6=3^{4+5+6}=3^{15}\)

b) \(5^2\times5^4\times5^5\times25=5^2\times5^4\times5^5\times5^2=5^{2+4+5+2}=5^{13}\)

c) \(10^8\div10^3=10^{8-3}=10^5\)

d) \(a^7\div a^2=a^{7-2}=a^5\)

2.

\(987=900+80+7\\ =9\times100+8\times10+7\\ =9\times10^2+8\times10^1+7\times10^0\)

\(2021=2000+20+1\\ =2\times1000+2\times10+1\times1\\ =2\times10^3+2\times10^1+1\times10^0\)

\(abcde=a\times10000+b\times1000+c\times100+d\times10+e\times1\\ =a\times10^4+b\times10^3+c\times10^2+d\times10^1+e\times10^0\)

còn bài 2

Đề thiếu, bạn coi lại đề.

1.Phép cộng:

giao hoán: a + b = b + a

Kết hợp : (a + b) + c = a + ( b + c)

Phép nhân:

Giao hoán: a . b = b . a

Kết hợp: (a . b) . c = a( b . c)

2, Luỹ thừa bậc n của a là tích của n thừa số, mỡi thừa số bằng a

3, Nhân hai luỹ thừa cùng cơ số: aⁿ . a^m = a^n+m

chia hai luỹ thừa cùng cơ số: aⁿ : a^m = a^n-m ( n lớn hơn hoặc bằng m, n khác 0)

1 

2 là n số tự nhiên a nhân với nhau

3 a^m/a^n=a^m-n ( phép chia )

  a^m*a^n=a^m+n

52.57 = 52+7 = 59