Question

State True or False.

Evaluate: $\frac{a^{2n+1}\times a^{(2n+1)(2n-1)}}{a^{n(4n-1)}\times (a^2{)}^{2n+3}}$, then answer is $\frac{1}{a^{n+6}}$.

• A. True
• B. False

Answer 1

The correct option is A True

Given expression $\frac{a^{2n+1}\times a^{(2n+1)(2n-1)}}{a^{n(4n-1)}\times (a^2{)}^{2n+3}}$
$=\frac{a^{2n+1}\times a^{4n^2-1}}{a^{4n^2-n}\times a^{4n+6}}$
Using rule of $a^m\times a^n=a^{m+n}$
$=\frac{a^{4n^2-1-4n^2+n}}{a^{4n+6-2n-1}}$
$=\frac{a^{n-1}}{a^{2n+5}}$
$=\frac{1}{a^{2n+5-n+1}}$ [Since, $\frac{a^m}{a^n}=\frac{1}{a^{n-m}}$]
$=\frac{1}{a^{n+6}}$
Thus, simplified form of given expression is $\frac{1}{a^{n+6}}$.