Question

Терміново 3 приклади і кінці 4,5,6 даю 100 балів

Answer 1

$\boxed{\begin{array}{lcl}(a^n)^k=a^{nk}\\\\a^n\cdot a^k=a^{k+n}\end{array}}$

$4)\ \ -1\dfrac35m^4n^3\bigg(-\dfrac12m^3p^6\bigg)^3=-\dfrac85m^4n^3\bigg(-\dfrac12\bigg)^3m^{3\cdot3}p^{6\cdot3}=$

$=-\dfrac85\bigg(-\dfrac18\bigg)m^{4+9}n^3p^{18}=\dfrac15m^{13}n^3p^{18}=0.2m^{13}n^3p^{18}$

$5)\ \ 2\dfrac14a^5b\bigg(\dfrac23ab^3\bigg)^3=\dfrac94a^5b\cdot\dfrac{2^3}{3^3}a^3b^9=\dfrac94\cdot\dfrac{4\cdot2}{9\cdot3}a^8b^{10}=\dfrac23a^8b^{10}$

$6)\ \ (-5a^3b^7)^3\bigg(-\dfrac15a^2c^6\bigg)^2=-5^3a^9b^{21}\cdot\dfrac1{5^2}a^4c^{12}=-5a^{13}b^{21}c^{12}$

Answer 2

Ответ:

$4)\ \ -1\dfrac{3}{5}\, m^4n^3\cdot \Big(-\dfrac{1}{2}\, m^3p^6\Big)^3=-\dfrac{8}{5}\, m^4n^3\cdot \Big(-\dfrac{1}{8}\, m^9\, p^{18}\Big)=\dfrac{1}{5}\, m^{13}\, n^{3}\, p^{18}$

$\displaystyle 5)\ \ 2\frac{1}{4}\, a^5b\cdot \Big(\frac{2}{3}\, ab^3\Big)^3=\frac{9}{4}\, a^5\, b\cdot \frac{8}{27}\, a^3\, b^9=\frac{2}{3}\, a^8\, b^{10}\\\\\\6)\ \ (-5a^3b^7)^3\cdot \Big(-\frac{1}{5}\, a^2\, c^6\Big)^2=-125\, a^9\, b^{21}\cdot \frac{1}{25}\, a^4\, c^{12}=-5\, a^{13}\, b^{21}\, c^{12}$