Question

Ребзя помогите решить карточку плачу 85 балов

Answer 1

$\displaystyle\tt\boxed{1}\\\\(xb)^{11}=x^{11}b^{11}\\\\ (-b^8)^4=(b^8)^4= b^{8\cdot4}=b^{32}\\\\ \bigg( \frac{2}{3}ay\bigg)^3=\frac{2^3}{3^3}\cdot a^3\cdot y^3=\frac{8}{27} a^3y^3\\\\ ((a^4)^3)^2=a^{4\cdot3\cdot2}=a^{24}$

$\displaystyle\tt\boxed{2}\\\\ a^{12}x^{12}=(ax)^{12}\\\\ 81b^4=3^4\cdot b^4=(3b)^4\\\\ \frac{16}{625}a^8b^4= \bigg(\frac{2^4}{5^4}\bigg)\cdot(a^2)^4\cdot b^4=\bigg(\frac{2}{5}a^2b\bigg)^4$

$\displaystyle\tt\boxed{3}\\\\ (-aa^6)^4=(-a)^4\cdot(a^6)^4=a^4\cdot a^{24}=a^{28}\\\\ (a^9)^3\cdot a^6=a^{27}\cdot a^6=a^{33}\\\\ (a^8)^2\cdot(a^5)^3=a^{16}\cdot a^{15}=a^{31}$

$\displaystyle\tt\boxed{4}\\\\ 0.4^6\cdot2.5^6=(0.4\cdot2.5)^6=1^6=1\\\\ 12.5^6\cdot0.8^6=(12.5\cdot0.8)^6=10^6=1000000\\\\ \frac{3^7\cdot(3^5)^2}{3^9\cdot81}=\frac{3^7\cdot3^{10}}{3^9\cdot3^4}=\frac{3^{17}}{3^{13}}=3^4=81$