Съкратетете дробите при a различно от 0 и b различно от 0

[Петя79]

а) 3^3 × a^10/9× a^8
б) 5^3 × a^3 × b^4/25× a^2×b^3
в) 2×3^n+7×3^n/3^n+2
г) 2^n+2^n/2^ n+1
д) 3^k+2/3^k +3^k+3^k

[S.B.]

а) 3^3 × a^10/9× a^8
б) 5^3 × a^3 × b^4/25× a^2×b^3
в) 2×3^n+7×3^n/3^n+2
г) 2^n+2^n/2^ n+1
д) 3^k+2/3^k +3^k+3^k

а) [tex]\frac{3^{3}.a^{10}}{9.a^{8}} = \frac{3^{3}.a^{10}}{3^{2}.a^{8}} = 3.a^{2}[/tex]

б) [tex]\frac{5^{3}.a^{3}.b^{4}}{25.a^{2}.b^{3}} = \frac{5^{3}.a^{3}.b^{4}}{5^{2}.a^{2}.b^{3}} = 5ab[/tex]

в) [tex]\frac{2.3^{n} + 7.3^{n}}{3^{n + 2}} = \frac{3^{n}(2 + 7)}{3^{n +2}} = \frac{3^{n}3^{2}}{3^{n + 2}} = \frac{3^{n + 2}}{3^{n + 2}} = 1[/tex]

г) [tex]\frac{2^{n} + 2^{n}}{2^{n + 1}} = \frac{2.2^{n}}{2^{n + 1}} = \frac{2^{1}.2^{n}}{2^{n + 1}} = \frac{2^{n + 1}}{2^{n + 1}} = 1[/tex]

д) [tex]\frac{3^{k + 2}}{3^{k} + 3^{k} + 3^{k}} = \frac{3^{k + 2}}{3.3^{k}} = \frac{3^{k + 2}}{3^{1}.3^{k} } = \frac{3^{k + 2}}{3^{k + 1}} = 3[/tex]