479. 1) 6abc:(-3c); 3) (-12pqr):6p; 480. 1) 15ab:(-5ab); 3) (-12mn):4mn; 481. 1) a^8:a^3; 4) c^5:c^4; 482. 1) y^8:(-y); 4) n^10:n^9; 483. 1) a^m:a^n; 484. 1) a^(m+1):a^m; 3) x^(n+1):x^(n-1); 485. 1) 8a^3b:2ab; 3) 16x^3y^3:4x^2y; 486. 1) 4a^4b^3c:(-5abc); 487. 1) (-2/3 a^4x^2y^3):( -1/3 a^3xy^2); 2) (-3/4 a^3b^2c): 1 1/2 a^2b^2c. 488. 1) 0,4 x^7y^5z^4:(-0,5 x^3y^2z^4); 2) (-1,2 a^6b^4c^4):(-0,3 a^3b^3c^3). 489. 1) 0,5a^5b^3c^2:( -2/3 a^3bc); 2) 1,5x^(n-1)y^(n-1): 3x^(n-2)y^(n-2). 490. 1) 0,12 x^(m-n)y^(n-1):(-0,6 x^(m-2n)y^(n-2)); 2) 1,8 a^(n+1)b^(n+2)c^(n+3):0,9 a^n b^(n+1)c^n. В следующих упражнениях записать частное двух алгебраических выражений в виде дроби: 491. 1) a:b; 2) a:5; 3) 8:c; 4) 2m:3n. 492. 1) -7d:(-2c); 2) 5a^4b:4pq; 3) 15x^2y^2: 4a^2b^2.

Решение:

1. \( 479. \)
• \( 1) \quad \frac{6abc}{-3c} = -2ab \)
• \( 3) \quad \frac{-12pqr}{6p} = -2qr \)
2. \( 480. \)
• \( 1) \quad \frac{15ab}{-5ab} = -3 \)
• \( 3) \quad \frac{-12mn}{4mn} = -3 \)
3. \( 481. \)
• \( 1) \quad \frac{a^8}{a^3} = a^{8-3} = a^5 \)
• \( 4) \quad \frac{c^5}{c^4} = c^{5-4} = c^1 = c \)
4. \( 482. \)
• \( 1) \quad \frac{y^8}{-y} = -y^{8-1} = -y^7 \)
• \( 4) \quad \frac{n^{10}}{n^9} = n^{10-9} = n^1 = n \)
5. \( 483. \)
• \( 1) \quad \frac{a^m}{a^n} = a^{m-n} \)
6. \( 484. \)
• \( 1) \quad \frac{a^{m+1}}{a^m} = a^{(m+1)-m} = a^1 = a \)
• \( 3) \quad \frac{x^{n+1}}{x^{n-1}} = x^{(n+1)-(n-1)} = x^{n+1-n+1} = x^2 \)
7. \( 485. \)
• \( 1) \quad \frac{8a^3b}{2ab} = 4a^{3-1}b^{1-1} = 4a^2b^0 = 4a^2 \)
• \( 3) \quad \frac{16x^3y^3}{4x^2y} = 4x^{3-2}y^{3-1} = 4xy^2 \)
8. \( 486. \)
• \( 1) \quad \frac{4a^4b^3c}{-5abc} = -\frac{4}{5}a^{4-1}b^{3-1}c^{1-1} = -\frac{4}{5}a^3b^2c^0 = -\frac{4}{5}a^3b^2 \)
9. \( 487. \)
• \( 1) \quad \frac{-2/3 a^4x^2y^3}{-1/3 a^3xy^2} = \frac{-2/3}{-1/3} \frac{a^4}{a^3} \frac{x^2}{x} \frac{y^3}{y^2} = 2a^{4-3}x^{2-1}y^{3-2} = 2axy \)
• \( 2) \quad \frac{-3/4 a^3b^2c}{3/2 a^2bc} = \frac{-3/4}{3/2} \frac{a^3}{a^2} \frac{b^2}{b} \frac{c}{c} = -\frac{3}{4} \cdot \frac{2}{3} a^{3-2}b^{2-1}c^{1-1} = -\frac{1}{2}ab \)
10. \( 488. \)
• \( 1) \quad \frac{0,4 x^7y^5z^4}{-0,5 x^3y^2z^4} = \frac{0,4}{-0,5} \frac{x^7}{x^3} \frac{y^5}{y^2} \frac{z^4}{z^4} = -0,8x^{7-3}y^{5-2}z^{4-4} = -0,8x^4y^3 \)
• \( 2) \quad \frac{-1,2 a^6b^4c^4}{-0,3 a^3b^3c^3} = \frac{-1,2}{-0,3} \frac{a^6}{a^3} \frac{b^4}{b^3} \frac{c^4}{c^3} = 4a^{6-3}b^{4-3}c^{4-3} = 4a^3bc \)
11. \( 489. \)
• \( 1) \quad \frac{0,5a^5b^3c^2}{-2/3 a^3bc} = \frac{1/2}{-2/3} \frac{a^5}{a^3} \frac{b^3}{b} \frac{c^2}{c} = \frac{1}{2} \cdot \left(-\frac{3}{2}\right) a^{5-3}b^{3-1}c^{2-1} = -\frac{3}{4}a^2b^2c \)
• \( 2) \quad \frac{1,5x^{n-1}y^{n-1}}{3x^{n-2}y^{n-2}} = \frac{1,5}{3} \frac{x^{n-1}}{x^{n-2}} \frac{y^{n-1}}{y^{n-2}} = 0,5x^{(n-1)-(n-2)}y^{(n-1)-(n-2)} = 0,5x^{n-1-n+2}y^{n-1-n+2} = 0,5xy \)
12. \( 490. \)
• \( 1) \quad \frac{0,12 x^{m-n}y^{n-1}}{-0,6 x^{m-2n}y^{n-2}} = \frac{0,12}{-0,6} \frac{x^{m-n}}{x^{m-2n}} \frac{y^{n-1}}{y^{n-2}} = -0,2x^{(m-n)-(m-2n)}y^{(n-1)-(n-2)} = -0,2x^{m-n-m+2n}y^{n-1-n+2} = -0,2x^n y \)
• \( 2) \quad \frac{1,8 a^{n+1}b^{n+2}c^{n+3}}{0,9 a^n b^{n+1}c^n} = \frac{1,8}{0,9} \frac{a^{n+1}}{a^n} \frac{b^{n+2}}{b^{n+1}} \frac{c^{n+3}}{c^n} = 2a^{(n+1)-n}b^{(n+2)-(n+1)}c^{(n+3)-n} = 2a^1b^1c^3 = 2abc^3 \)
13. \( 491. \)
• \( 1) \quad \frac{a}{b} \)
• \( 2) \quad \frac{a}{5} \)
• \( 3) \quad \frac{8}{c} \)
• \( 4) \quad \frac{2m}{3n} \)
14. \( 492. \)
• \( 1) \quad \frac{-7d}{-2c} = \frac{7d}{2c} \)
• \( 2) \quad \frac{5a^4b}{4pq} \)
• \( 3) \quad \frac{15x^2y^2}{4a^2b^2} \)