KnowledgeBoat Logo
|

Mathematics

Simplify:

a2n+3.a(2n+1)(n+2)(a3)2n+1.an(2n+1)\dfrac{a^{2n+3}.a^{(2n+1)(n+2)}}{(a^3)^{2n+1}.a^{n(2n+1)}}

Exponents

9 Likes

Answer

a2n+3.a(2n+1)(n+2)(a3)2n+1.an(2n+1)=a2n+3.a2n2+4n+n+2a3(2n+1).a2n2+n=a2n+3.a2n2+5n+2a6n+3.a2n2+n=a(2n+3)+(2n2+5n+2)a(6n+3)+(2n2+n)=a2n+3+2n2+5n+2a6n+3+2n2+n=a2n2+7n+5a2n2+7n+3=a(2n2+7n+5)−(2n2+7n+3)=a2n2+7n+5−2n2−7n−3=a2\dfrac{a^{2n+3}.a^{(2n+1)(n+2)}}{(a^3)^{2n+1}.a^{n(2n+1)}}\\[1em] = \dfrac{a^{2n+3}.a^{2n^2+4n+n+2}}{a^{3(2n+1)}.a^{2n^2+n}}\\[1em] = \dfrac{a^{2n+3}.a^{2n^2+5n+2}}{a^{6n+3}.a^{2n^2+n}}\\[1em] = \dfrac{a^{(2n+3)+(2n^2+5n+2)}}{a^{(6n+3)+(2n^2+n)}}\\[1em] = \dfrac{a^{2n+3+2n^2+5n+2}}{a^{6n+3+2n^2+n}}\\[1em] = \dfrac{a^{2n^2+7n+5}}{a^{2n^2+7n+3}}\\[1em] = a^{(2n^2+7n+5)-(2n^2+7n+3)}\\[1em] = a^{2n^2+7n+5-2n^2-7n-3}\\[1em] = a^{2}\\[1em]

a2n+3.a(2n+1)(n+2)(a3)2n+1.an(2n+1)=a2\dfrac{a^{2n+3}.a^{(2n+1)(n+2)}}{(a^3)^{2n+1}.a^{n(2n+1)}} = a^2

Answered By

8 Likes

Related Questions