Упр.284 ГДЗ Муравин 7 класс (Алгебра)

1) M/(24a^5 b^13) = 5/6b; 3) M^2/(20a^13 b^18) = (2b)^2/5a;
2) (48x^12 b^16)/M = 8x^2/5; 4) (56x^15 y^15)/M^3 = 7x^3/8y^3.

1. $$\frac{M}{24a^5b^{13}}=\frac{5}{6b}$$
   $$M\cdot 6b=24a^5b^{13}\cdot 5$$
   $$M=\frac{24a^5b^{13}\cdot 5}{6b}=20a^5b^{12}$$
2. $$\frac{48x^{12}b^{16}}{M}=\frac{8x^2}{5}$$
   $$M\cdot 8x^2=48x^{12}b^{16}\cdot 5$$
   $$M=\frac{48x^{12}b^{16}\cdot 5}{8x^2}=30x^{10}b^{16}$$
3. $$\frac{M^2}{20a^{13}b^{18}}=\frac{(2b)^2}{5a}$$
   $$M^2\cdot 5a=20a^{13}b^{18}\cdot (2b)^2$$
   $$M^2=\frac{20a^{13}b^{18}\cdot 4b^2}{5a}=16a^{12}b^{20}$$
   $$M^2=(4a^6b^{10})^2$$
   Значит,
   $$M=4a^6b^{10}$$
   или
   $$M=-4a^6b^{10}$$
4. $$\frac{56x^{15}y^{15}}{M^3}=\frac{7x^3}{8y^3}$$
   $$M^3\cdot 7x^3=56x^{15}y^{15}\cdot 8y^3$$
   $$M^3=\frac{56x^{15}y^{15}\cdot 8y^3}{7x^3}=64x^{12}y^{18}$$
   $$M^3=(4x^4y^6)^3$$
   Значит,
   $$M=4x^4y^6$$

Ответ

1) $$20a^5b^{12}$$; 2) $$30x^{10}b^{16}$$; 3) $$4a^6b^{10}$$ или $$-4a^6b^{10}$$; 4) $$4x^4y^6$$.