Question

Решите пример со всеми действиями

Answer 1

$1)\ \ \dfrac{18x^3}{7b^4}\cdot \dfrac{14b}{9x^2}=\dfrac{2x\cdot 2}{b^3}=\dfrac{4x}{b^3}\\\\\\2)\ \ \dfrac{9x}{10b^2}\cdot \dfrac{5b^3}{3x^3}=\dfrac{3\cdot b}{2\cdot x^2}\\\\\\3)\ \ \dfrac{2}{9a^2-b^2}\cdot (6a-2b)=\dfrac{2\cdot 2\, (3a-b)}{(3a-b)(3a+b)}=\dfrac{4}{3a+b}$

$4)\ \ \dfrac{3}{a^2-4b^2}\cdot (5a+10b)=\dfrac{3\cdot 5(a+2b)}{(a-2b)(a2b)}=\dfrac{15}{a-2b}\\\\\\5)\ \ \Big(-\dfrac{2a^4}{3b^2}\Big)^3=-\dfrac{8a^{12}}{27b^6}\\\\\\6)\ \ \Big(-\dfrac{3a^5}{4b^3}\Big)^2=\dfrac{9a^{10}}{16b^6}$

$7)\ \ \dfrac{x^3-16x}{3xy}\cdot \dfrac{6y}{2x+8}=\dfrac{x\, (x-4)(x+4)}{x}\cdot \dfrac{2}{2\, (x+4)}=x-4$

$8)\ \ \dfrac{4xy}{x^2-5x}\cdot \dfrac{2x^2-50}{8y}=\dfrac{x\cdot 2(x-5)(x+5)}{x\cdot (x-5)\cdot 2}=x+5\\\\\\9)\ \ -\dfrac{c^3+7c^2}{2b}:\dfrac{49-c^2}{4b^2}=-\dfrac{c^2\cdot (c+7)\cdot 4b^2}{2b\cdot (7-c)(7+c)}=-\dfrac{2b\cdot c^2}{7-c}=\dfrac{2bc^2}{c-7}$

$10)\ \ \dfrac{c^2-36}{9b^3}:\Big(-\dfrac{6c+c^2}{3b^2}\Big)=-\dfrac{(c-6)(c+6)}{9b^3}\cdot \dfrac{3b^2}{c\, (6+c)}=-\dfrac{c-6}{3b\cdot c}=\dfrac{6-c}{3bc}$

Answer 2

a)

18x³*14b/(7b⁴*9x²)=4x/b³

б)

(9х*5b³)/(10b²*3x³)=3b/2x²

в)

2*2(3a-b)/((3a-b)*(3a+b))=4/(3a+b);

г)

3*5(a+2b)/((a+2b)*(a-2b))=15/(a-2b)

и)

-с²(с+7)*4b²/(2b*((с+7)*(-с+7))=-2c²b/(7-c)=2bc²/(c-7)

д)

(-2а⁴/3b²)³=-8a¹²/27b⁶

е)

(-3a⁵/4b³)²=9a¹⁰/(16b⁶)

ж)

((х³-16х)/(3ху))*(6у/(2х+8))=(х*(х-4)*(х+4)*6у)/(3ху*(2*(х+4))=(х-4)

з)

4ху*2*(х-5)*(х+5)/((х*(х-5)*8у)=(х+5)

к)

-((с²-36)*3b²)/(c*(6+c)(9b³))=(6-c)*(6+c)/(3bc*(6+c))=(6-c)/(3bc)