\(\frac{2^{35}.9^{25}.5^{25}.13^{22}.7^{16}.5^{16}}{9^{26}.13^{22}5.^{22}.7^{17}.4^{17}.5^{2.9}}=2^{\left(35-2.17\right)}.9^{\left(25-26\right)}.5^{\left(25+16\right)-\left(22+2.9\right)}.13^{22-22}.7^{16-17}.\)

\(2^1.9^{-1}.5^1.13^0.7^{-1}=\frac{2.5}{9.7}=\frac{10}{63}\)

- Ôi dễ vãi ~~

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 ~

\(\frac{2^{35}.45^{25}.13^{22}.35^{16}}{9^{26}.65^{22}.28^{17}.25^9}=\frac{2^{35}.5^{25}.9^{25}.13^{22}.5^{16}.7^{16}}{9^{26}.5^{22}.13^{22}.4^{17}.7^{17}.5^9.5^9}=\frac{2^{35}.5^3.5^7}{9.\left(2^2\right)^{17}.7.5^9}=\frac{2^{35}.5^3}{9.2^{34}.7.5^2}=\frac{2.5}{9.7}=\frac{10}{63}\)

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:

\(\dfrac{-1}{2}x^ny^{n-2}:\left(-3x^{n-2}y^n\right)\)

\(=\dfrac{1}{6}x^{n-n+2}y^{n-2-n}\)

\(=\dfrac{1}{6}x^2y^{-2}\)

\(A=\dfrac{2^{35}.45^{25}.13^{22}.35^{16}}{9^{26}.65^{22}.28^{17}.25^9}=\dfrac{2^{35}.3^{50}.5^{25}.13^{22}.5^{16}.7^{16}}{3^{52}.13^{22}.5^{22}.2^{34}.7^{17}.5^{18}}\)

\(=\dfrac{2.5^3}{3^2.5^2.7}=\dfrac{2.5}{3^2.7}=\dfrac{10}{63}\)