Question

5.9. Найдите значение выражения:
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Answer 1

$1)\; \; a=-0,5\; \; ,\; \; b=2\\\\(a^4\, b^5)^2:(a^2\, b^2)^3=\frac{a^8\, b^{10}}{a^6\, b^6}=a^2\, b^4=(-0,5)^2\cdot 2^4=(-\frac{1}{2})^2\cdot 2^4=\frac{2^4}{2^2}=2^2=4\\\\\\2)\; \; x=-3\; \; ,\; \; y=\frac{2}{3}\\\\(x^7y^4)^3:(x^{10}y^5)^2=\frac{x^{21}\, y^{12}}{x^{20}\, y^{10}}=x\, y^2=-3\cdot (\frac{2}{3})^2=-\frac{3\cdot 4}{9}=-\frac{4}{3}=-1\frac{1}{3}$

Answer 2

1)

(а⁴в⁵)² : (а²в²)³ =

= а⁴°² в⁵°² : а²°³ в²°³ =

= а⁸в¹⁰ : а⁶в⁶ =

= а⁸⁻⁶ * в¹⁰⁻⁶ =

= а²в⁴,

при а = -0,5,  в = 2:

(-0,5)² * 2⁴ = 0,25 * 16 = 4,

2)

(х⁷у⁴)³ : (х¹⁰у⁵)² =

= х⁷°³ у⁴°³ : х¹⁰°² у⁵°² =

= х²¹у¹² : х²⁰у¹⁰ =

= х²¹⁻²⁰ * у¹²⁻¹⁰ =

= х¹*у² = ху²,

при х = -3,  у = 2/3:

-3 * (2/3)² = -3 * 4/9 = -4/3 = - 1 1/3