Question

Помогите решить пожалуйста!!!

Answer 1

Ответ:

$1)\ \displaystyle \frac{a^9\cdot a^{12}}{a^{18}}= \frac{a^{9+12}}{a^{18}}=\frac{a^{21}}{a^{18}}=a^{21-18}=a^{3}= 4^3=\boxed{64.}$

$2)\ \displaystyle \frac{a^{12}\cdot a^{6}}{a^{14}}= \frac{a^{12+6}}{a^{14}}=\frac{a^{18}}{a^{14}}=a^{18-14}=a^{4}= 3^4=\boxed{81.}$

$3)\ \displaystyle \frac{a^{11}\cdot a^{9}}{a^{18}}= \frac{a^{11+9}}{a^{18}}=\frac{a^{20}}{a^{18}}=a^{20-18}=a^{2}= 7^2=\boxed{49.}$

$4)\ \displaystyle \frac{a^{9}\cdot a^{8}}{a^{12}}= \frac{a^{9+8}}{a^{12}}=\frac{a^{17}}{a^{12}}=a^{17-12}=a^{5}= 2^5=\boxed{32.}$

$5)\ \displaystyle \frac{a^{16}\cdot a^{-7}}{a^{8}}= \frac{a^{16+(-7)}}{a^{8}}=\frac{a^{9}}{a^{8}}=a^{9-8}=a^{1}=a=\boxed{3.}$

$6)\ \displaystyle \frac{a^{18}\cdot a^{-6}}{a^{10}}= \frac{a^{18+(-6)}}{a^{10}}=\frac{a^{12}}{a^{10}}=a^{12-10}=a^{2}= 5^2=\boxed{25.}$

$7)\ \displaystyle \frac{a^{17}\cdot a^{-6}}{a^{9}}= \frac{a^{17+(-6)}}{a^{9}}=\frac{a^{11}}{a^{9}}=a^{11-9}=a^{2}= 4^2=\boxed{16.}$

$8)\ \displaystyle \frac{a^{19}\cdot a^{-11}}{a^{5}}= \frac{a^{19+(-11)}}{a^{5}}=\frac{a^{8}}{a^{5}}=a^{8-5}=a^{3}= 5^3=\boxed{125.}$

$9)\ \displaystyle \frac{(a^4)^5}{a^{18}}= \frac{a^{4\cdot5}}{a^{18}}=\frac{a^{20}}{a^{18}}=a^{20-18}=a^{2}= 6^2=\boxed{36.}$

$10)\ \displaystyle \frac{(a^8)^2}{a^{11}}= \frac{a^{8\cdot2}}{a^{11}}=\frac{a^{16}}{a^{11}}=a^{16-11}=a^{5}= 2^5=\boxed{32.}$

$11)\ \displaystyle \frac{(a^8)^2}{a^{13}}= \frac{a^{8\cdot2}}{a^{13}}=\frac{a^{16}}{a^{13}}=a^{16-13}=a^{3}= 5^3=\boxed{125.}$

$12)\ \displaystyle \frac{(a^3)^5}{a^{11}}= \frac{a^{3\cdot5}}{a^{11}}=\frac{a^{15}}{a^{11}}=a^{15-11}=a^{4}= 3^4=\boxed{81.}$

Объяснение:

Смотри свойства степеней на фотографии.