Question

Dau 15 puncte + coronita + stelute + multumesc+ cerere de prietenie!!!!!!!!!!Utilizand formula a supra b: c supra d=a supra b * d supra c= a*d supra b*c calculati:
A)2^n*3^(m+1) supra 5^(p+2) :2^(n+2)*3^(m+1) supra 5^p=
B)a*x*y supra b*z*t : a*y*z supra b*x*t =
C) abab supra cd : cdcd supra ab=

Answer 1

$a)~ \frac{2^n \cdot 3^{m+1}}{5^{p+2}}: \frac{2^{n+2} \cdot 3^{m+1}}{5^p} = \frac{2^n \cdot 3^{m+1}}{5^{p} \cdot 5^2} \cdot \frac{5^p}{2^{n+2} \cdot 3^{m+1}} = \frac{2^n \cdot 3^{m+1}}{5^2} \cdot \frac{1}{2^n \cdot 3^{m+1} \cdot 2^2 \cdot 3} = \\ \\ = \frac{1}{5^2 \cdot 2^2 \cdot 3}= \frac{1}{300} . \\ \\ b)~ \frac{axy}{bzt} : \frac{ayz}{bxt}= \frac{\not ax \not y}{ \not bz \not t} \cdot \frac{\not bx \not t}{\not a \not yz}= \frac{x^2}{z^2}.$

$c)~ \frac{\overline{abab}}{\overline{cd}}: \frac{\overline{cdcd}}{\overline{ab}} = \frac{\overline{abab}}{\overline{cd}} \cdot \frac{\overline{ab}}{\overline{cdcd}}= \frac{100 \cdot \overline{ab} + \overline{ab}}{ \overline{cd}} \cdot \frac{ \overline{ab}}{100 \cdot \overline{cd}+ \overline{cd}}= \frac{101 \cdot \overline{ab}}{\overline{cd}} \cdot \frac{\overline{ab}}{101 \cdot \overline{cd}}= \\ \\ = \frac{\overline{ab}^2}{\overline{cd}^2}.$