Question

Помогите номера 7 , 16, 18.

Answer 1

Ответ:

$7)\ \ \ \displaystyle \frac{\dfrac{(x^2)^3\cdot (x^7)^2\cdot x^3\cdot x^8}{x\cdot (x^5)^3\cdot x^2}}{x^{13}}=\dfrac{x^6\cdot x^{14}\cdot x^{11}}{x\cdot x^{15}\cdot x^2\cdot x^{13}}=\frac{x^{31}}{x^{31}}=1$

$16)\ \ \ \displaystyle \frac{100\cdot 2^{n}\cdot (5^2)^{n}}{2^{n-2}\cdot 5^{2n+1}}=\frac{5^2\cdot 2^2\cdot 2^{n}\cdot 5^{2n}}{2^{n-2}\cdot 5^{2n+1}}=\frac{5^{2n+2}\cdot 2^{n+2}}{2^{n-2}\cdot 5^{2n+1}}=5^{2n+2-2n-1}\cdot 2^{n+2-n+2}=\\\\=5^1\cdot 2^4=5\cdot 16=80\\\\\\18)\ \ \ \frac{147\cdot (7^{n})^2\cdot 9^{n}\cdot 3^2}{3^{2n+2}\cdot 7^{2n+1}}=\frac{7^2\cdot 3\cdot 7^{2n}\cdot 3^{2n}\cdot 3^2}{3^{2n+2}\cdot 7^{2n+1}}=\frac{7^{2n+2}\cdot 3^{2n+3}}{3^{2n+2}\cdot 7^{2n+1}}=\frac{7\cdot 3}{1}=21$

Answer 2

Объяснение:

$7)\ \frac{\frac{(x^2)^3*(x^7)^2*x^3*x^8}{x*(x^5)^3*x^2} }{x^{13}} =\frac{\frac{x^6*x^{14}*x^{11}}{x^3*x^{15}} }{x^{13}}=\frac{\frac{x^{31}}{x^{18}} }{x^{13}}=\frac{x^{13}}{x^{13}}= 1.\\\\16)\ \frac{100*2^n*(5^2)^n}{2^{n-2}*5^{2n+1}}=\frac{25*4*2^n*5^{2n} }{2^{n-2}*5^{2n+1}}=\frac{5^2*2^2*2^n*5^{2n}}{2^{n-2}*5^{2n+1}} = \frac{2^{n+2}*5^{2n+2}}{2^{n-2}*5^{2n+1}} =\\= 2^{n+2-(n-2)}*5^ {2n+2-(2n+1)}=2^{n+2-n+2}*5^{2n+2-2n-1}=2^4*5^1=16*5=80.$

$18)\ \frac{147*(7^n)^2*9^n*3^2}{3^{2n+2}*7^{2n+1}}=\frac{49*3*7^{2n}*(3^2)^n*3^2}{3^{2n+2}*7^{2n+1}}=\frac{7^2*3^1*7^{2n}*3^{2n}*3^2}{3^{2n+2}*7^{2n+1}} =\frac{3^{2n+3}*7^{2n+2}}{3^{2n+2}*7^{2n+1}}=\\=3^{2n+3-(2n+2)}*7^{2n+2-(2n+1)}=3^{2n+3-2n-2}*7^{2n+2-2n-1}=3^1*7^1=21.$