Question

WRITE 3^n/9^n-1 AS A POWER OF 3

Answer 1

Answer:

$\frac{3^n}{9^{n-1}} =$  $3^{-n+2}$

Step-by-step explanation:

Required to find,

$\frac{3^n}{9^{n-1}}$ as a power of 3

Recall the formula

1. $(a^m)^n = a^{mn}$
2. $\frac{a^m}{a^n } = a^{m-n}$

Solution:

$\frac{3^n}{9^{n-1}}$ = $\frac{3^n}{(3^2)^{n-1}}$

Applying the formula,$(a^m)^n = a^{mn}$ we get

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

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

∴ $\frac{3^n}{9^{n-1}} =$  $3^{-n+2}$

#SPJ2

Answer 2

To find :

• $\frac{3^{n} }{9^{n-1} }$ as the power of 3

solution :

Formula to be used :

• $(x^{m} )^{n}=x^{mn}$.....(1)
• $\frac{x^{m} }{x^{n} }=x^{m-n}$......(2)

solution :

$\frac{3^{n} }{9^{n-1} }=\frac{3^{n} }{(3^{2} )^{n-1}}$.......(3)

Applying formula 1 in equation 3 we get ,

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

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

therefore , $\frac{3^{n} }{9^{n-1} }=3^{-n+2}$

#SPJ2