Question

(243^n/5*3^2n+1)/ 9^n*3^n-1 =?
Can someone solve this equation and show me how?

Answer 1

i hope this will usful to u

Answer 2

Answer:

$\frac{3^{5-5n}}{5}$

Step-by-step explanation:

In the question,

We have been given the term to solve,

$\frac{\frac{243^{n}}{5.3^{2n+1}}}{9^{n}\times 3^{n-1}}$

So, on solving the equation using the BODMAS rule, we get,

$\frac{243^{n}}{5.3^{2n+1}}\times \frac{1}{9^{n}\times 3^{n-1}}=\frac{3^{5}}{15.3^{2n}\times 3^{2n}\times 3^{n-1}}=\frac{3^{5}}{5(3^{2n+1}\times 3^{2n}\times 3^{n-1})}$

Now, we also know that,

xᵃ × xᵇ = xᵃ⁺ᵇ

Therefore, on using the same identity in the equation, we get,

$\frac{3^{5}}{5(3^{2n+1}\times 3^{2n}\times 3^{n-1})}=\frac{3^{5}}{5(3^{5n})}\\\frac{3^{5}}{5(3^{5n})}=\frac{3^{5-5n}}{5}$

Because,

$\frac{a^{m}}{a^{n}}=a^{m-n}$

Therefore, the final solution of the equation on simplifying is given by,

$\frac{\frac{243^{n}}{5.3^{2n+1}}}{9^{n}\times 3^{n-1}}=\frac{3^{5-5n}}{5}$