Question

3n*9^n+1÷3^n-1*9^n-1

Answer 1

Answer:

243

Step-by-step explanation:

3^n × 9^n + 1/3^n - 1 × 9^n - 1

3^n × (3^2)^n + 1 / 3^n - 1 × (3^2)^n - 1

3^n × 3^2n + 2/ 3^n - 1 × 3^2n - 2

3^n + 2n + 2/ 3^n - 1 + 2n - 2

3^3n + 2/3^3n - 3

3^3n + 2 - 3n + 3

3^5

243

Answer 2

By the product rule of exponent, we can say that $a^{m+n}=a^m\times a^n$

Given $3^n\times 9^{n+1}\div(3^{n-1}\times 9^{n-1})$

we can write it as

$3^n\times (3\times 3)^{n+1}\div (3^{n-1}\times (3\times 3)^{n-1})$

by using product rule and further calculation we get

$=3^n\times (3)^{2n+2}\div (3^{n-1}\imes (3)^{2(n-1)})$

$=3^n\times (3)^{2n+2}\div (3^{n-1}\imes (3)^{2n-2})$

on further calculation we get

$=3^{n+2n+2}\div 3^{n-1+2n-2}$

$=3^{3n+2}\div 3^{3n-3}$

$=3^{3n+2-3n+3}$

$=3^5$

$=243$

The required solution for the given equation is 243.

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