3(3^2x – (1/3)^-2x)

Since its not an equation I assume you are trying to simplify the statement, correct? Allright, we’ll go from that.

The easiest way to simplify something is to go to the innermost term and start working. Since the “innermost term” here is a subtraction problem, well, we can choose which expression.

The 3^2x seems to be in simplest form already, so we’ll leave it for now and work onthat last term, shall we?

(1/3)^(-2x)

Definition of a negative exponent (a^-1 = 1/a)

(1/3)^(-2x)=(3^-1)^(-2x)

Power of a power { (x^m)^n = x^(mn) }

3^ (-1*-2x)

3^2x

Now, we rewrite the problem

3(3^2x – 3^2x)

Definition of Subtraction

3(3^2x + -(3^2x))

Definition of Additive Inverse { a + -a = 0}

3(0)

Multiplication by zero

0

So, for any value of x

3(3^2x – (1/3)^(-2x)) = 0