Задание 2. Найдите значение выражения: 1) 1 √16⋅x⁶y⁴ при x=2, y=5; 2) 1 √25⋅x⁶y² при x=3, y=5; 3) 1 √4⋅x²y⁸ при x=5, y=2; 4) 1 √9⋅x⁴y¹⁰ при x=3, y=2; 5) 1 √4⋅x⁸y⁴ при x=2, y=3; 6) 1 √25⋅x⁴y⁸ при x=5, y=2; 7) 1 √9⋅x²y⁶ при x=7, y=3; 8) 1 √16⋅x¹⁰y² при x=2, y=3.

1) \[\frac{1}{\sqrt{16 \cdot x^6 y^4}} = \frac{1}{4 \cdot |x^3| \cdot y^2}\]

Подставим x = 2, y = 5:

\[\frac{1}{4 \cdot |2^3| \cdot 5^2} = \frac{1}{4 \cdot 8 \cdot 25} = \frac{1}{800}\]

2) \[\frac{1}{\sqrt{25 \cdot x^6 y^2}} = \frac{1}{5 \cdot |x^3| \cdot |y|}\]

Подставим x = 3, y = 5:

\[\frac{1}{5 \cdot |3^3| \cdot |5|} = \frac{1}{5 \cdot 27 \cdot 5} = \frac{1}{675}\]

3) \[\frac{1}{\sqrt{4 \cdot x^2 y^8}} = \frac{1}{2 \cdot |x| \cdot y^4}\]

Подставим x = 5, y = 2:

\[\frac{1}{2 \cdot |5| \cdot 2^4} = \frac{1}{2 \cdot 5 \cdot 16} = \frac{1}{160}\]

4) \[\frac{1}{\sqrt{9 \cdot x^4 y^{10}}} = \frac{1}{3 \cdot x^2 \cdot |y^5|}\]

Подставим x = 3, y = 2:

\[\frac{1}{3 \cdot 3^2 \cdot |2^5|} = \frac{1}{3 \cdot 9 \cdot 32} = \frac{1}{864}\]

5) \[\frac{1}{\sqrt{4 \cdot x^8 y^4}} = \frac{1}{2 \cdot x^4 \cdot y^2}\]

Подставим x = 2, y = 3:

\[\frac{1}{2 \cdot 2^4 \cdot 3^2} = \frac{1}{2 \cdot 16 \cdot 9} = \frac{1}{288}\]

6) \[\frac{1}{\sqrt{25 \cdot x^4 y^8}} = \frac{1}{5 \cdot x^2 \cdot y^4}\]

Подставим x = 5, y = 2:

\[\frac{1}{5 \cdot 5^2 \cdot 2^4} = \frac{1}{5 \cdot 25 \cdot 16} = \frac{1}{2000}\]

7) \[\frac{1}{\sqrt{9 \cdot x^2 y^6}} = \frac{1}{3 \cdot |x| \cdot |y^3|}\]

Подставим x = 7, y = 3:

\[\frac{1}{3 \cdot |7| \cdot |3^3|} = \frac{1}{3 \cdot 7 \cdot 27} = \frac{1}{567}\]

8) \[\frac{1}{\sqrt{16 \cdot x^{10} y^2}} = \frac{1}{4 \cdot |x^5| \cdot |y|}\]

Подставим x = 2, y = 3:

\[\frac{1}{4 \cdot |2^5| \cdot |3|} = \frac{1}{4 \cdot 32 \cdot 3} = \frac{1}{384}\]