Упр.334 ГДЗ Колягин Ткачёва 7 класс (Алгебра)

1) (-9/7)^8 :(-9/7)^5;
2) (1/17)^18 :(1/17)^17;
3) x^21 :x^7;
4) d^24 :d^12.
Найти значение выражения:
1) 7(a-5)-b(5-a) при a=2,b=3;
2) a(a-b)+b(b-a) при a=6,3,b=2,3;
3) 2x(x+y)-3y(x+y)+7(x+y) при x=4,y=5;
4) x(y-x)-y(x-y)-4(y-x) при x=3,y=-5.

1. $$\left(-\frac{9}{7}\right)^8 : \left(-\frac{9}{7}\right)^5 = \left(-\frac{9}{7}\right)^{8-5} = \left(-\frac{9}{7}\right)^3.$$
2. $$\left(\frac{1}{17}\right)^{18} : \left(\frac{1}{17}\right)^{17} = \left(\frac{1}{17}\right)^{18-17} = \frac{1}{17}.$$
3. $$x^{21} : x^7 = x^{21-7} = x^{14}.$$
4. $$d^{24} : d^{12} = d^{24-12} = d^{12}.$$
5. $$7(a-5)-b(5-a), \quad a=2,\ b=3$$
   $$5-a=-(a-5),$$
   $$7(a-5)-b(5-a)=7(a-5)+b(a-5)=(a-5)(7+b).$$
   $$ (2-5)(7+3)=-3\cdot 10=-30.$$
6. $$a(a-b)+b(b-a), \quad a=6{,}3,\ b=2{,}3$$
   $$b-a=-(a-b),$$
   $$a(a-b)+b(b-a)=a(a-b)-b(a-b)=(a-b)(a-b)=(a-b)^2.$$
   $$ (6{,}3-2{,}3)^2=4^2=16.$$
7. $$2x(x+y)-3y(x+y)+7(x+y), \quad x=4,\ y=5$$
   $$2x(x+y)-3y(x+y)+7(x+y)=(x+y)(2x-3y+7).$$
   $$ (4+5)(2\cdot 4-3\cdot 5+7)=9(8-15+7)=9\cdot 0=0.$$
8. $$x(y-x)-y(x-y)-4(y-x), \quad x=3,\ y=-5$$
   $$x(y-x)-y(x-y)-4(y-x)=x(y-x)+y(y-x)-4(y-x).$$
   $$=(y-x)(x+y-4).$$
   $$(-5-3)(3+(-5)-4)=-8\cdot(-6)=48.$$

Ответ

1. $$\left(-\frac{9}{7}\right)^3$$
2. $$\frac{1}{17}$$
3. $$x^{14}$$
4. $$d^{12}$$
5. $$-30$$
6. $$16$$
7. $$0$$
8. $$48$$