Răspuns:
Explicație pas cu pas:
1)
[tex](\frac{3a^2b^2}{5x^2y^2} )^3*(\frac{2ax^2}{5b^3y})^2:(\frac{4a^4}{5b^2y^4} )^2 =[/tex]
[tex]=\frac{(3a^2b^2)^3}{(5x^2y^2)^3} *\frac{(2ax^2)^2}{(5b^3y)^2}*\frac{(5b^2y^4)^2}{(4a^4)^2} =[/tex]
[tex]=\frac{3^3a^6b^6}{5^3x^6y^6} *\frac{2^2a^2x^4}{5^2b^6y^2}*\frac{5^2b^4y^8}{4^2a^8} =[/tex]
[tex]=\frac{2^2 3^3 5^2 a^6 a^2 b^6 b^4 x^4 y^8} {4^2 5^3 5^2 a^8 b^6 x^6 y^2 y^6}=[/tex]
[tex]=\frac{2^2 3^3 5^2 a^8 b^{10} x^4 y^8} {2^4 5^5 a^8 b^6 x^6 y^8}=[/tex]
[tex]=\frac{ 3^3 b^4 } {2^2 5^3 x^2}[/tex]
2)
[tex](\frac{m + n}{a + b} )^3*(\frac{n - m}{a - b})^3*(\frac{a^2 - b^2}{m^2 - n^2} )^2 =[/tex]
[tex]=\frac{(m + n)^3}{(a + b)^3}*\frac{(n - m)^3}{(a - b)^3}*\frac{(a^2 - b^2)^2}{(m^2 - n^2)^2}=[/tex]
[tex]=\frac{(m + n)^3}{(a + b)^3}*\frac{(n - m)^3}{(a - b)^3}*\frac{[(a - b)(a + b)]^2}{[(m - n)(m + n)]^2}=[/tex]
[tex]=\frac{(m + n)^3}{(a + b)^3}*\frac{(n - m)^3}{(a - b)^3}*\frac{(a - b)^2(a + b)^2}{(m - n)^2(m + n)^2}=[/tex]
[tex]=\frac{(m + n)^3(n - m)^3(a - b)^2(a + b)^2}{(a + b)^3(a - b)^3(n-m)^2(m + n)^2}=[/tex]
[tex]=\frac{(m + n)(n - m)}{(a + b)(a - b)}=\frac{n^2 - m^2}{a^2 - b^2}[/tex]
