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

a) 5⁴ : 5² + 3² . 3³

= 5² + 3⁵ = 25 + 243 = 268

Học tốt!!!

a) 5⁴:5²+3².3³=5² + 3⁵=25+243 = 278

b) 3+6+9+12+...+96

=3.1+3.2+3.3+3.4+...+3.32

=3.(1+2+3+4+...+32)

=3.\(\frac{\left(32+1\right).32}{2}\)=\(3.33.16=1584\)

a)\(\frac{2}{3}+\frac{3}{4}+\frac{5}{6}\)

\(=\frac{8+9+10}{12}\)

\(=\frac{27}{12}=\frac{9}{4}\)

b)\(\frac{15}{8}-\frac{7}{12}+\frac{5}{6}\)

\(=\frac{45-14+20}{24}\)

\(=\frac{51}{24}=\frac{17}{8}\)

2)

a)\(\frac{2}{5}+\frac{7}{13}+\frac{3}{5}+\frac{1}{7}\)

\(=\frac{2}{5}+\frac{3}{5}+\frac{7}{13}+\frac{1}{7}\)

\(=1+\frac{7}{13}+\frac{1}{7}\)

\(=\frac{20}{13}+\frac{1}{7}\)

\(=\frac{153}{91}\)

Tí tớ trả lời tiếp

b)\(5\frac14+3\frac25-4\frac14\)

=\(\left(5\frac14-4\frac14\right)+3\frac25\)

=\(\left\lbrack\left(5-4\right)+\left(\frac14-\frac14\right)\right\rbrack+\frac{17}{5}\)

=\(1+0+\frac{17}{5}\)

=\(\frac55+\frac{17}{5}\)

=\(\frac{22}{5}\)

B1a)\(11\frac34-\left(6\frac56-4\frac12\right)+1\frac23\)

=\(11\frac34-6\frac56+4\frac12+1\frac23\)

=\(\left(11-6+4+1\right)+\left(\frac34-\frac56+\frac12+\frac23\right)\)

=\(10+\left(\frac{9}{12}-\frac{10}{12}+\frac{6}{12}+\frac{8}{12}\right)\)

=\(10+\left(-\frac{1}{12}+\frac{6}{12}+\frac{8}{12}\right)\)

=10+\(\frac{13}{12}\)

=\(\frac{120}{12}+\frac{13}{12}\)

=\(\frac{133}{12}\)

b)\(2\frac{17}{20}-1\frac{11}{5}+6\frac{9}{20}:3\)

= \(\frac{57}{20}-\frac{16}{5}+\frac{129}{20}\times\frac13\)

=\(\frac{57}{20}-\frac{16}{5}+\frac{129}{60}\)

=\(\frac{171}{60}-\frac{192}{60}+\frac{129}{60}\)

=\(\frac{108}{60}\)

=\(\frac95\)

a)=\(\frac{7}{30}\)-\(\frac{17}{12}\)=\(\frac{-71}{60}\)                                                                                                                                        b) = \(\frac{29}{20}\)+\(\frac{-31}{30}\)+\(\frac{-2}{3}=\frac{-1}{4}\)

a) 22 + 3 . 2³ = 22 + 3 . 8 = 22 + 24 = 46

b) 41 . 67 + 33 . 41 = 41 . ( 67 + 33 ) = 41 . 100 = 4100

c) 322 . 5 - [ 622 : 4 + 2 . ( 11 - 8) ] = 322 . 5 - [ 622 : 4 + 2 . 3 ] = 322 . 5 - [ 155,5 + 6 ] = 322 . 5 - 161,5 = 1610 + 161,5 = 1448,5

\(4.\left\{3^2.\left[\left(5^2+2^3\right):11\right]-26\right\}+2009\)

\(=4.\left\{9.\left[\left(25^{ }+8\right):11\right]-26\right\}+2009\)

\(=4.\left\{9.\left[33:11\right]-26\right\}+2009\)

\(=4.\left\{9.3-26\right\}+2009\) \(=4.\left(27-26\right)+2009\)

\(=4.1+2009=2013\)

3.Tìm x biết:

a) \(2-x=17-\left(-5\right)\)

\(2-x=22\)

\(x=2-22\)

\(x=-20\)

Vậy \(x=-20\)

b) \(2x-6=-3-\left(-7\right)\)

\(2x-6=4\)

\(2x=6+4\)

\(2x=10\)

\(x=10:2\)

\(x=5\)

Vậy \(x=5\)

c) \(\left(3x-6\right).3=3^4\)

\(\left(3x-6\right).3=81\)

\(3x-6=81:3\)

\(3x-6=27\)

\(3x=27+6\)

\(3x=33\)

\(x=33:3\)

\(x=11\)

Vậy \(x=11\)

\(M=\frac{-3}{4}.\frac{2}{11}+\frac{-3}{4}.\frac{9}{11}+2\frac{3}{4}\)

\(M=\frac{-3}{22}+\frac{-27}{44}+\frac{2\times4+3}{4}\)

\(M=\frac{-3}{22}+\frac{-27}{44}+\frac{11}{4}\)

\(M=\frac{-6}{44}+\frac{-27}{44}+\frac{121}{44}\)

\(M=\frac{-33}{44}+\frac{121}{44}\)

\(M=2\)