Question

simplify: x^2n+3 .x^(2n+1)(n+2) upon (x^3)^2n+1 .x^n(2n+1)​

Answer 1

Let us know some indices rules first:

$\quad\quad$• $a^{b}*a^{c}=a^{b+c}$

$\quad\quad$• $a^{b}/a^{c}=a^{b-c}$

$\quad\quad$• $(a^{b})^{c}=a^{bc}$

Now we solve the problem:

$\therefore \dfrac{x^{2n+3}.x^{(2n+1)(n+2)}}{(x^{3})^{2n+1}.x^{n(2n+1)}}$

$=\dfrac{x^{2n+3+(2n+1)(n+2)}}{x^{6n+3+n(2n+1)}}$

$=\dfrac{x^{2n+3+2n^{2}+5n+2}}{x^{6n+3+2n^{2}+n}}$

$=\dfrac{x^{2n^{2}+7n+5}}{x^{2n^{2}+7n+3}}$

$=x^{2n^{2}+7n+5-2n^{2}-7n-3}$

$=x^{2}$

$\Rightarrow \dfrac{x^{2n+3}.x^{(2n+1)(n+2)}}{(x^{3})^{2n+1}.x^{n(2n+1)}}=x^{2}$

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