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

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

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

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

\(=4.1+2009=2013\)

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) 5 . 4² – 18 : 3² = 5 . 16 - 18 : 9 = 80 - 2 = 78;

b) 3³ . 18 – 3³ . 12 = 27 . 18 - 27 . 12 = 486 - 324 = 162;

Lưu ý. Có thể áp dụng tính chất phân phối của phép nhân đối với phép cộng:

3³ . 18 – 3³ . 12 = 3³ (18 - 12) = 27 . 6 = 162;

c) 39 . 213 + 87 . 39 = 39 . (213 + 87) = 39 . 300 = 11700;

d) 80 – [130 – (12 – 4)²] = 80 - (130 - 64) = 80 - 66 = 14.

a)=78

b)=162

c)=11700

d)=14

a)\(0,2:1\frac{3}{5}+80\%=\frac{1}{8}+80\%=\frac{3205}{32}\)

b)\(0,5:\frac{5}{4}-2\frac{1}{5}=\frac{2}{5}-\frac{11}{5}=-\frac{9}{5}\)

\(0,2:1\frac{3}{5}+80\%=\left(\frac{2}{10}+\frac{8}{5}\right)+80\%=\left(\frac{20}{100}+\frac{160}{100}\right)+80\%=\frac{180}{100}+80\%=180\%+80\%=260\%\)

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: \(=36:4+2\cdot25=9+50=59\)

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) \(\left(-0,75+\frac{1}{2}\right):\frac{4}{3}\)

\(=\frac{-1}{4}:\frac{4}{3}\)

\(=\frac{-3}{16}\)

b) \(\frac{5}{9}.\frac{2}{7}+\frac{5}{9}.\frac{5}{7}-\frac{8}{3}\)

\(=\frac{5}{9}.\left(\frac{2}{7}+\frac{5}{7}\right)-\frac{8}{3}\)

\(=\frac{5}{9}.1-\frac{8}{3}\)

\(=\frac{-19}{9}\)

c)  \(7,5.1\frac{3}{4}-6\frac{2}{5}\)

\(=\frac{15}{2}.\frac{7}{4}-\frac{32}{5}\)

\(=\frac{269}{40}\)