Verified answer

Объяснение:

№7

m¹⁵(n⁶)³ / (mn)¹⁷ = m¹⁵n¹⁸ / m¹⁷n¹⁷ = n/(m²)

m = 5; n = 15

n/(m²) = 15/(5²) = 15/25 = 3/5

№8

х¹⁴(у³)⁵ / (ху)¹³ = х¹⁴у¹⁵/х¹³у¹³ = ху¹⁵/у¹³ = ху²

х = 10; у = 7

ху² = 10 * 7² = 10 * 49 = 490

№9

а¹⁶(в⁷)³/(ав)¹⁸ = а¹⁶в²¹/а¹⁸в¹⁸ = а¹⁶в³/а¹⁸ = в³/а²

а = 2; в = 6

в³/а² = 6³/2² = 216/4 = 54

7)

[tex] \frac{ {m}^{15} ( {n}^{6} ) {}^{3} }{(mn) {}^{17} } = \frac{m {}^{15} n {}^{18} }{m {}^{17} n {}^{17} } = \frac{n}{ {m}^{2} } = \\ = \frac{15}{5 {}^{2} } = \frac{15}{25} = \frac{3}{5} = 0.6[/tex]

8)

[tex] \frac{ {x}^{14}(y {}^{3} ) {}^{5} }{(xy) {}^{13} } = \frac{ {x}^{14}y {}^{15} }{x {}^{13} {y}^{13} } = x {y}^{2} = \\ = 10 \times {7}^{2} = 10 \times 49 = 490[/tex]

9)

[tex] \frac{ {a}^{16} (b {}^{7} ) {}^{3} }{(ab) {}^{18} } = \frac{ {a}^{16} {b}^{21} }{ {a}^{18} {b}^{18} } = \frac{ {b}^{3} }{ {a}^{2} } = \\ = \frac{ {6}^{3} }{ {2}^{2} } = \frac{216}{4} = 54[/tex]

Использовались свойства степени:

[tex](x {}^{a} ) {}^{b} = x {}^{ab} \\ (xy) {}^{a} = {x}^{a} \times {y}^{a} [/tex]