Rút gọn phân thức
\(\frac{2^{35}\cdot45^{25}\cdot13^{22}\cdot35^{16}}{28^{17}\cdot9^{26}\cdot65^{22}\cdot25^9}\)
Bài 1) Tìm giá trị lớn nhất của biểu thức Q=\(-8x^2+4xy-y^2+10\)
Bài 2) Rút gọn biểu thức sau dưới dạng phân số tối giản
\(\frac{2^{35}\cdot45^{25}\cdot13^{22}\cdot35^{16}}{9^{26}\cdot65^{22}\cdot28^{17}\cdot25^9}\)
Bài 3) Tổng các số nguyên thỏa mãn /x/<2016
Rút gọn phân số: \(\frac{2^{35}.45^{25}.13^{22}.35^{16}}{9^{26}.65^{22}.28^{17}.25^9}\) ( Nhập dưới dạng phân số tối giản )
\(\frac{2^{35}.9^{25}.5^{25}.13^{22}.7^{16}.5^{16}}{9^{26}.13^{22}5.^{22}.7^{17}.4^{17}.5^{2.9}}=2^{\left(35-2.17\right)}.9^{\left(25-26\right)}.5^{\left(25+16\right)-\left(22+2.9\right)}.13^{22-22}.7^{16-17}.\)
\(2^1.9^{-1}.5^1.13^0.7^{-1}=\frac{2.5}{9.7}=\frac{10}{63}\)
Rút gọn:
\(\frac{2^{35}.45^{25}.13^{22}.35^{16}}{9^{26}.65^{22}.28^{17}.25^9}\)
Ta có:
\(\frac{2^{35}.45^{25}.13^{22}.35^{16}}{9^{26}.65^{22}.28^{17}.25^9}=\frac{2^{35}.\left(9.5\right)^{25}.13^{22}.\left(5.7\right)^{16}}{9^{26}.\left(5.13\right)^{22}.\left(7.4\right)^{17}.\left(5.5\right)^9}\)
\(=\frac{2^{35}.9^{25}.5^{25}.13^{22}.5^{16}.7^{16}}{9^{26}.13^{22}.5^{22}.7^{17}.4^{17}.5^9.5^9}\)
\(=\frac{2^{35}.5^3}{9.4^{17}.5^2.7}\)
\(=\frac{2^{35}.5}{9.4^{17}.7}\)
\(=\frac{2^{35}.5}{9.2^{34}.7}\)
\(=\frac{2.5}{9.7}\)
\(=\frac{10}{63}\)
p/s: - Ko chắc ~
\(\frac{2^{35}.45^{25}.13^{22}.35^{16}}{9^{26}.65^{22}.28^{17}.25^9}=\frac{2^{35}.5^{25}.9^{25}.13^{22}.5^{16}.7^{16}}{9^{26}.5^{22}.13^{22}.4^{17}.7^{17}.5^9.5^9}=\frac{2^{35}.5^3.5^7}{9.\left(2^2\right)^{17}.7.5^9}=\frac{2^{35}.5^3}{9.2^{34}.7.5^2}=\frac{2.5}{9.7}=\frac{10}{63}\)
1)Số tự nhiên n để \(x^6y^{n+2}\) chia hết cho \(x^ny^4z^{n-3}\)
2) Rút gọn phân số \(\frac{2^{35}.45^{25}.13^{22}.35^{16}}{9^{26}.65^{22}.28^{17}.25^9}\)
Câu 1: Rút gọn biểu thức : \(\dfrac{2^{35}\cdot45^{25}\cdot13^{22}\cdot35^{16}}{9^{26}\cdot65^{22}\cdot28^{17}\cdot25^9}\)
Câu 2:Tìm x : \(\left(4\cdot\left(z+y\right)\cdot x^3-3\left(z+y\right)\cdot x^2-\left(z+y\right)\right):\left(z+y\right)-4x^3+3x^2+2x-4=0\)
Câu 3: Cho A= 9x2+4y2+54x-36y-12y+90.A đạt GTNN tại x=ay+b.Khi đó a+b ......
Câu 4: Rút gọn K=(x2y-3)2-(2x-y)3+xy2(6-x3)+8x3-6x2y-y3
Câu 5: Tính (\(\dfrac{-1}{2}x^ny^{n-2}\)):(-3xn-2yn)
Câu 6: Tìm x |x|<2016
Câu 7: GTNN A= 9x2-6xy+2y2+5
Câu 1:
\(\dfrac{2^{35}.45^{25}.13^{22}.35^{16}}{9^{26}.65^{22}.28^{17}.25^9}\)
\(=\dfrac{2^{35}.9^{25}.5^{25}.13^{22}.7^{16}.5^{16}}{9^{26}.13^{22}.5^{22}.2^{17}.2^{17}.7^{17}.5^9.5^9}\)
Bạn rút gọn sẽ còn lại:
\(=\dfrac{2.5}{7.9}=\dfrac{10}{63}\)
Câu 4:
\(K=\left(x^2y-3\right)^2-\left(2x-y\right)^3+xy^2\left(6-x^3\right)+8x^3-6x^2y-y^3\)\(K=\left(x^2y\right)^2-2.x^2y.3+3^2-\left[\left(2x\right)^3-3.\left(2x\right)^2.y+3.2x.y^2-y^3\right]+6xy^3-x^4y^2+8x^3-6x^2y-y^3\)\(K=x^4y^2-6x^2y+9-8x^3+12x^2y-6xy^2+y^3+6xy^2-x^4y^2+8x^3-6x^2y-y^3\)\(K=9\)
Câu 5:
\(\dfrac{-1}{2}x^ny^{n-2}:\left(-3x^{n-2}y^n\right)\)
\(=\dfrac{1}{6}x^{n-n+2}y^{n-2-n}\)
\(=\dfrac{1}{6}x^2y^{-2}\)
Rút gọn :\(\frac{2\cdot3\cdot5+4\cdot9\cdot25+6\cdot9\cdot35+10\cdot21\cdot40}{2\cdot3\cdot5+4\cdot9\cdot35+6\cdot9\cdot49+10\cdot21\cdot56}\)
Rút gọn:
\(\dfrac{2^{35}.45^{25}.13^{22}.35^{16}}{9^{26}.65^{22}.28^{17}.25^9}\) = ...
\(A=\dfrac{2^{35}.45^{25}.13^{22}.35^{16}}{9^{26}.65^{22}.28^{17}.25^9}=\dfrac{2^{35}.3^{50}.5^{25}.13^{22}.5^{16}.7^{16}}{3^{52}.13^{22}.5^{22}.2^{34}.7^{17}.5^{18}}\)
\(=\dfrac{2.5^3}{3^2.5^2.7}=\dfrac{2.5}{3^2.7}=\dfrac{10}{63}\)
Rút gọn biểu thức \(Q=\frac{\left(17\frac{8}{19}-16\frac{9}{18}\right)\left(17,5+16\frac{17}{51}+32\frac{15}{22}\right)}{\frac{7}{3\cdot13}+\frac{7}{13\cdot23}+\frac{7}{23\cdot33}}\) rồi tính 20% của Q ta đc bao nhiêu?
Rút gọn biểu thức \(Q=\frac{\left(17\frac{8}{19}-16\frac{9}{18}\right)\left(17,5+16\frac{17}{51}+32\frac{15}{22}\right)}{\frac{7}{3\cdot13}+\frac{7}{13\cdot23}+\frac{7}{23\cdot33}}\) rồi tính 20% của Q ta đc bao nhiêu?