Simplify - i-a2n-3-a2n-1n-2-a3 2n-1-an2n-1-ii-x2n-7-x2 3n-2-x42n-3

(i) a^2n 3.a^(2n+1)(n+2)/(a^3 )^2n+1.a^n(2n+1) Given expression=a^2n+3.a^2n^2+4n+n+2/a^6n+3.a^2n^2+n =a^2n+3+2n^2+5n+2/a^6n+3+2n^2+n=a^2n^2+7n+5/a^2n^2+7n+3 ...

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Byju's Answer

Standard VIII

Mathematics

Exponents with like Bases

Simplify : i ...

Question

Simplify :

$(i) \frac{a^{2 n - 3} . a^{(2 n + 1) (n + 2)}}{{(a^{3})}^{2 n + 1} . a^{n (2 n + 1)}} (i i) \frac{x^{2 n + 7} . {(x^{2})}^{3 n + 2}}{x^{4 (2 n + 3)}}$

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Solution

$(i) \frac{a^{2 n - 3} . a^{(2 n + 1) (n + 2)}}{{(a^{3})}^{2 n + 1} . a^{n (2 n + 1)}} Given expression= \frac{a^{2 n + 3} . a^{2 n^{2} + 4 n + n + 2}}{a^{6 n + 3} . a^{2 n^{2} + n}} = \frac{a^{2 n + 3 + 2 n^{2} + 5 n + 2}}{a^{6 n + 3 + 2 n^{2} + n}} = \frac{a^{2 n^{2} + 7 n + 5}}{a^{2 n^{2} + 7 n + 3}} = \frac{a^{(2 n^{2} + 7 n + 3) + 2}}{a^{2 n^{2} + 7 n + 3}} = a^{2} (i i) \frac{x^{2 n + 7} . {(x^{2})}^{3 n + 2}}{x^{4 (2 n + 3)}} Given expression= \frac{x^{2 n + 7} . x^{6 n + 4}}{x^{8 n + 12}} = \frac{x^{2 n + 7 + 6 n + 4}}{x^{8 n + 12}} = \frac{x^{8 n + 11}}{x^{8 n + 12}} = x^{8 n + 11 - 8 n - 12} = x^{- 1} = \frac{1}{x}$

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Similar questions

Q. If

{(1 + x + x^{2})}^{n} = a_{0} + a_{1} x + a_{2} x^{2} . . . . + a_{2 n} x^{2 n}

, then

Q. If

a_{1}, a_{2}, a_{3}, . . . . a_{2 n + 1}

are in A.P. then

\frac{a_{2 n + 1} - a_{1}}{a_{2 n + 1} + a_{1}} + \frac{a_{2 n} - a_{2}}{a_{2 n} + a_{2}} + . . . + \frac{a_{n + 2} - a_{n}}{a_{n + 2} + a_{n}}

is equal to

Q. If

{(1 + x + x^{2})}^{n} = a_{0} + a_{1} x + a_{2} x^{2} + . . . + a_{2 n} x^{2 n}

, then

a_{0} + a_{3} + a_{6} + . . . =

Q. Given that

{(1 + x + x^{2})}^{n} = a_{0} + a_{1} x + a_{2} x^{2} + \dots + a_{2 n} x^{2 n},

find the values of
(i)

a_{0} + a_{1} + a_{2} + \dots . + a_{2 n}

(ii)

a_{0} - a_{1} + a_{2} - a_{3} \dots . . + a_{2 n}

Q. If

a_{1,} a_{2,} a_{3,} . . . . . . . . a_{2 n + 1}

are in A.P. then

\frac{a_{2 n + 1} - a_{1}}{a_{2 n + 1} + a_{1}} + \frac{a_{2 n + 1} - a_{2}}{a_{2 n + 1} + a_{2}} + . . . . . . + \frac{a_{2 n + 1} - a_{n}}{a_{2 n + 1} + a_{n}}

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Simplify : (i) a2n−3.a(2n+1)(n+2)(a3)2n+1.an(2n+1)(ii) x2n+7.(x2)3n+2x4(2n+3)

(i) a2n−3.a(2n+1)(n+2)(a3)2n+1.an(2n+1)Given expression=a2n+3.a2n2+4n+n+2a6n+3.a2n2+n=a2n+3+2n2+5n+2a6n+3+2n2+n=a2n2+7n+5a2n2+7n+3=a(2n2+7n+3)+2a2n2+7n+3=a2(ii) x2n+7.(x2)3n+2x4(2n+3)Given expression=x2n+7.x6n+4x8n+12=x2n+7+6n+4x8n+12=x8n+11x8n+12=x8n+11−8n−12=x−1=1x

Simplify :

$(i) \frac{a^{2 n - 3} . a^{(2 n + 1) (n + 2)}}{{(a^{3})}^{2 n + 1} . a^{n (2 n + 1)}} (i i) \frac{x^{2 n + 7} . {(x^{2})}^{3 n + 2}}{x^{4 (2 n + 3)}}$