Hãy nhập câu hỏi của bạn vào đây, nếu là tài khoản VIP, bạn sẽ được ưu tiên trả lời.
\(16^6:4^2=2^{24}:2^4=2^{24-4}=2^{20}\)
\(12^n:2^{2n}=12^n:4^n=3^n\)
\(27^8:9^4=3^{24}:3^8=3^{24-8}=3^{16}\)
\(125^5:25^3=5^{15}:5^6=5^{15-6}=5^9\)
\(4^{14}.5^{28}=4^{14}.25^{14}=\left(4.25\right)^{14}=100^{14}\)
\(64^4.16^5:4^{20}=2^{24}.2^{20}:2^{40}=2^{24+20-40}=2^4=16\)
1. a) 3^2 .2^2 .2^4 = 3^2. 2^(2+4)=3^2. 2^6
b) 10^2. 10^3.10^5= 10^(2+3+5)= 10^10
c) x.x^5=x^(1+5)=x^6
d) a^3 .a^2 ,a^5= a^(3+2+5)= a^10
2. a) 2^3 và 3^2 . Ta có: 2^3 = 8, 3^2=9 => 2^3 < 3^2
b) 2^4 và 4^2. Ta có: 2^4= 16, 4^2=16 => 2^4 = 4^2
c) 2^5 và 5^2. Ta có: 2^5= 32, 5^2=25 => 2^5 > 5^2
d) 2^100 và 100. => 2^100 > 100
3. a) 3^8:3^4= 3^(8-4)=3^4
b) 10^8:10^2=10^(8-6)=10^2
c) a^6: a (a#0) = a^(6-1)=a^5
a) a mũ 4 chia a = a mũ 3
b) ( 16 mũ 2 ) / ( 4 mũ 2 )
= ( 16 / 4 ) mũ 2
= 4 mũ 2
= 16
c) ( 25 mũ 2 ) / ( 5 mũ 2 )
= ( 25 / 5 ) mũ 2
= 5 mũ 2
= 25
\(a^4:a=a^3\)
\(16^2:4^2=\left(16:4\right)^2=4^2=16\)
\(25^2:5^2=\left(25:5\right)^2=5^2=25\)
a) a3.a5 = a3+5 = a8
b) x7.x.x4 = x7+1+4 = x12
c) 35.45 = (3.4)5 = 125
d) 85.23 = 25.25.25.23 = 25+5+5+3 = 218
a/a\(^3\).a\(^5\)=a\(^8\)
b/x\(^7\).x.x\(^4\)=x\(^{12}\)
c/3\(^5\).4\(^5\)=2\(^{10}\).3\(^5\)
d/8\(^5\).2\(^3\)=2\(^{18}\)
Bài 1.
a) \(\dfrac{3}{14}.\dfrac{7}{20}+\dfrac{13}{20}=\dfrac{3}{40}+\dfrac{13}{20}=\dfrac{3}{40}+\dfrac{26}{40}=\dfrac{29}{40}\).
b) \(\left(2.3^{2010}+12.3^{2010}-3.3^{2010}\right):3^{2012}\)
\(=3^{2010}\left(2+12-3\right):3^{2012}\)
\(=3^{2010}.11:3^{2012}\)
\(=\left(3^{2010}:3^{2012}\right).11\)
\(=\dfrac{1}{9}.11\)
\(=\dfrac{11}{9}\).
Bài 2.
a) \(\left(5^{14}.25^{10}\right):125^3\)
\(=\left[5^{14}.\left(5^2\right)^{10}\right]:\left(5^3\right)^3\)
\(=\left[5^{14}.5^{20}\right]:5^9\)
\(=5^{34}:5^9\)
\(=5^{25}\).
b) \(\left(\dfrac{1}{2}\right)^5.\left(\dfrac{1}{64}\right)^9:\left(\dfrac{1}{16}\right)^5\)
\(=\dfrac{1}{2^5}.\dfrac{1}{64^9}:\dfrac{1}{16^5}\)
\(=\dfrac{1}{2^5}.\dfrac{1}{\left(2^6\right)^9}:\dfrac{1}{\left(2^4\right)^5}\)
\(=\dfrac{1}{2^5}.\dfrac{1}{2^{54}}:\dfrac{1}{2^{20}}\)
\(=\dfrac{1}{2^{59}}:\dfrac{1}{2^{20}}\)
\(=\dfrac{2^{20}}{2^{59}}\)
\(=\dfrac{1}{2^{39}}\).
Lời giải:
\(2^{27}.3^{18}=(2^3)^9.(3^2)^9=8^9.9^9=(8.9)^9=72^9\)
\(25^4.2^8=25^4.(2^2)^4=25^4.4^4=(25.4)^4=100^4\)
\((-9)^4.27^2=9^4.27^2=(3^2)^4.(3^3)^2=3^8.3^6=3^{8+6}=3^{14}\)
\(-5^4:25=-5^4:(5^2)=-5^{4-2}=-5^2\)
a. \(5^{10}.125^2.625^3=5^{10}.\left(5^3\right)^2.\left(5^4\right)^3=5^{10}.5^6.5^{12}=5^{10+6+12}=5^{28}\)
a: \(=5^{10}\cdot5^6\cdot5^{12}=5^{28}\)
b: \(=10^3\cdot10^8\cdot10^{15}=10^{26}\)
c: \(=2^{20}\cdot2^{20}=2^{40}\)
d: \(=2^{16}\cdot2^{16}\cdot3^8=2^{32}\cdot3^8\)
e: \(=\dfrac{3^{24}}{3^8}=3^{16}\)
f: \(=2^{12}\cdot2^{20}\cdot2^5=2^{37}\)
a, \(6^5:6^2=6^{5-2}=6^3\)
b, \(2^3.4=2^3.2^2=2^{3+2}=2^5\)
c, \(5^5:25=5^5:5^2=5^{5-2}=5^3\)
d, \(49^3:7^4=7^6:7^4=7^{6-4}=7^2\)
e, \(a^9:a=a^{9-1}=a^8\)\(\left(a\ne0\right)\)
Chúc bạn học tốt!!!
a,65:62=65-2=63
b,23x4= 25
c,55:25=55:55=1
d,493:74= 72
e, a9:a=a9-1=a8
a: \(=36:4+2\cdot25=9+50=59\)
b: \(=79\left(82+18\right)=79\cdot100=7900\)
c: \(=49-9-\left(4^2+2^2\right)\)
\(=40-16-4=40-20=20\)
d: \(=16+\left[400:\left(200-42-138\right)\right]\)
\(=16+400:20=16+20=36\)
a) \(16^{3} \cdot 2^{4}\)
Ta có:
⇒ \(2^{12} \cdot 2^{4} = 2^{16}\)
✅ Đáp án: \(2^{16}\)
b) \(\frac{36^{5}}{18^{5}}\)
Ta có:
⇒ \(\frac{2^{10} \cdot 3^{10}}{2^{5} \cdot 3^{10}} = 2^{10 - 5} = 2^{5}\)
✅ Đáp án: \(2^{5}\)
c) \(5^{5} + 5^{2} \cdot 5^{3}\)
Ta có:
⇒ \(5^{5} + 5^{5} = 2 \cdot 5^{5}\)
✅ Đáp án: \(2 \cdot 5^{5}\)
d) \(\frac{125^{4}}{5^{8}}\)
Ta có:
⇒ \(\frac{5^{12}}{5^{8}} = 5^{12 - 8} = 5^{4}\)
✅ Đáp án: \(5^{4}\)
a; 16\(^3\).2\(^4\)
= (2\(^4\))\(^3\).2\(^4\)
= 2\(^{12}\).2\(^4\)
= 2\(^{16}\)
b; 36\(^5:18^5\)
= (36:18)\(^5\)
= 2\(^5\)
c; 24,5\(^5\) + 5\(^2\).5\(^3\) (xem lại đề bài)
d; 125\(^4\):5\(^8\)
=(5\(^3)^4\) : 5\(^8\)
= 5\(^{12}:5^8\)
= 5\(^4\)