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Exponents — MATHS STD 8 — Question

ICSE BoardEnglish MediumSTD 8MATHSExponents3 Marks
Question
Evaluate: $\frac{a^{2 n+1} \times a^{(2 n+1)(2 n-1)}}{a^{n(4 n-1)} \times\left(a^2\right)^{2 n+3}}$
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Answer

$ \frac{a^{2 n+1} \times a^{(2 n+1)(2 n-1)}}{a^{n(4 n-1)} \times\left(a^2\right)^{2 n+3}}$
$ =\frac{a^{2 n+1} \times a^{(2 n)^2-(1)^2}}{a^{4 n^2-n} \times a^{2(2 n+3)}}$
$ =\frac{a^{2 n+1} \times a^{4 n^2-1}}{a^{4 n^2-n} \times a^{4 n+6}}$
$ =a^{2 n+1+4 n^2-1-4 n^2+n-4 n-6}$
$ =a^{-n-6}$
$ =a^{-(-n+6)}$
$ =\frac{1}{a^{n+6}}$

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