solve without the use of the calculator.

Question

9^x+1-9^x-1/4.3^2x-3

Answer 1

We are given the expression:

(9^(x+1) - 9^(x-1)) / (4*3^(2x-3))

First, we can simplify the numerator by factoring out a common factor of 9^x:

9^x * (9 - 1) = 9^x * 8

Now the expression becomes:

(8*9^x) / (4*3^(2x-3))

Now, we can simplify the expression further by canceling out the common factors:
(8*9^x) = 8 * 3^2 * 3^x = 8 * 3^(x+2)

So the expression simplifies to:

(8*3^(x+2)) / (4*3^(2x-3)) = (2*3^(x+2)) / 3^(2x-3) = 2*3^5 = 486

Therefore, the simplified value of the expression is 486.