\(\frac{-2}{5}\) \(.\) \(\frac{1}{8}\) =  \(\frac{1}{8}\) \(.\) \(\frac{3}{5}\)=   \(\frac{3}{40}\)

 - Hok t - 

Trả lời :

\(-\frac{2}{5}\cdot\frac{1}{8}=\frac{1}{8}\cdot\frac{3}{5}=\frac{3}{40}\)

1k đê

~HT~

Câu 8:

Giải:
Ta có: \(a:b=3:4\Rightarrow\frac{a}{3}=\frac{b}{4}\Rightarrow\frac{a^2}{9}=\frac{b^2}{16}\)

Áp dụng tính chất dãy tỉ số bằng nhau ta có:

\(\frac{a^2}{9}=\frac{b^2}{16}=\frac{a^2+b^2}{9+16}=\frac{36}{25}\)

+) \(\frac{a^2}{9}=\frac{36}{25}\Rightarrow a^2=\frac{324}{25}\Rightarrow a=\pm\frac{18}{5}\)

+) \(\frac{b^2}{16}=\frac{36}{25}\Rightarrow b^2=\frac{576}{25}\Rightarrow b=\pm\frac{24}{5}\)

Vậy bộ số \(\left(x;y\right)\) là \(\left(\frac{18}{5};\frac{24}{5}\right);\left(\frac{-18}{5};\frac{-24}{5}\right)\)

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) \(3^{7} \cdot 27^{5} \cdot 81^{3}\)

• Đổi về cơ số 3: \(27 = 3^{3} , \textrm{ }\textrm{ } 81 = 3^{4}\).

\(3^{7} \cdot \left(\right. 3^{3} \left.\right)^{5} \cdot \left(\right. 3^{4} \left.\right)^{3} = 3^{7} \cdot 3^{15} \cdot 3^{12} = 3^{7 + 15 + 12} = 3^{34} .\)

b) \(100^{6} \cdot 1000^{5} \cdot 10 \textrm{ } 000^{3}\)

• Đổi về cơ số 10: \(100 = 10^{2} , \textrm{ }\textrm{ } 1000 = 10^{3} , \textrm{ }\textrm{ } 10 \textrm{ } 000 = 10^{4}\).

\(\left(\right. 10^{2} \left.\right)^{6} \cdot \left(\right. 10^{3} \left.\right)^{5} \cdot \left(\right. 10^{4} \left.\right)^{3} = 10^{12} \cdot 10^{15} \cdot 10^{12} = 10^{39} .\)

c) \(\frac{36^{5}}{18^{5}}\)

• Do cùng số mũ:

\(\left(\left(\right. \frac{36}{18} \left.\right)\right)^{5} = 2^{5} = 32.\)

d) \(24 \cdot 5^{2} + 5^{2} \cdot 5^{3}\)

\(= 24 \cdot 25 + 25 \cdot 125 = 600 + 3125 = 3725.\)

e) \(\frac{125^{4}}{5^{8}}\)

• Đổi về cơ số 5: \(125 = 5^{3}\).

\(\left(\right. 5^{3} \left.\right)^{4} : 5^{8} = 5^{12} : 5^{8} = 5^{12 - 8} = 5^{4} = 625.\)

TÓM lại là a) \(3^{34}\)
b) \(10^{39}\)
c) \(32\)
d) \(3725\)
e) \(625\)

bạn muốn chép đáp án hay sem cách làm///??

a: \(3^7\cdot27^5\cdot81^3\)

\(=3^7\cdot\left(3^3\right)^5\cdot\left(3^4\right)^3\)

\(=3^7\cdot3^{15}\cdot3^{12}=3^{7+15+12}=3^{34}\)

b: \(100^6\cdot1000^5\cdot10000^3\)

\(=\left(10^2\right)^6\cdot\left(10^3\right)^5\cdot\left(10^4\right)^3\)

\(=10^{12}\cdot10^{15}\cdot10^{12}=10^{15+12+12}=10^{39}\)

c: \(36^5:18^5=\left(\frac{36}{18}\right)^5=2^5=32\)

d: \(24\cdot5^2+5^2\cdot5^3\)

\(=5^2\left(24+5^3\right)\)

\(=25\cdot\left(24+125\right)=25\cdot149=3725\)

e: \(125^4:5^8=\left(5^3\right)^4:5^8=5^{12}:5^8=5^{12-8}=5^4\)

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) \(\left(\dfrac{1}{2}\right)^5.\left(\dfrac{1}{64}\right)^9:\left(\dfrac{1}{16}\right)^5\)

\(=\dfrac{1}{2^5}.\dfrac{1}{64^9}:\dfrac{1}{16^5}\)

\(=\dfrac{1}{2^5}.\dfrac{1}{\left(2^6\right)^9}:\dfrac{1}{\left(2^4\right)^5}\)

\(=\dfrac{1}{2^5}.\dfrac{1}{2^{54}}:\dfrac{1}{2^{20}}\)

\(=\dfrac{1}{2^{59}}:\dfrac{1}{2^{20}}\)

\(=\dfrac{2^{20}}{2^{59}}\)

\(=\dfrac{1}{2^{39}}\).

Phần I :

a) 8²⁰ và 7²⁰

vì 8>7 nên 8²⁰>7²⁰

b) 4²⁰ và 16²⁰

vì 4<16 nên 4²⁰<16²⁰

c) 27⁷= (3³)⁷= 3²¹

81⁵=( 3⁴)⁵=3²⁰

vì 21>20 nên 3²¹>3²⁰ hay 27⁷> 81⁵

e) 5²¹= 5²⁰ . 5

vì 5²⁰ . 5>5²⁰ . 4 nên 5²¹> 4 . 5²⁰

Bài 1 :

a,8²⁰ > 7²⁰

b, 4²⁰ = 16¹⁰

c, 27⁷ > 81⁵

d , 5⁵⁴ > 3⁸¹

e, 5²¹ > 4 . 5²⁰

f, 2²⁰ > 7.2¹⁷

Sách Giáo Khoa

Bài giải:

a) -500; b) -500; c) -500.

a) (-125).4 = -500

b) (-4).125 = -500

c) 4.(-125) = -500

\(7^9:7^7+3^3.3\)

\(=7^2+3^4\)

\(=49+81\)

\(=130\)

ko biết

b, Ta có: 125^80 = (5^2)^80 =5^160

               25^118=(5^2)^118=5^236

vì 5^160<5^236 nên :125^80<5^118

( kí hiệu này ^ là mũ )