Can you simplify (9x)^-2 = -81x^2

Is the equal sign meant to be a minus sign, such as:

(9x)^-2 -81x^2
If the equal sign is there, it would be an equation, which we usually solve and not simplify.

For
(9x)^-2 -81x^2
note that they are both perfect squares, and you can apply the identity:
a²-b²=(a+b)(a-b)
So
(9x)^-2 -81x^2
=(1/9x)² - (9x)²
=(1/9x + 9x)(1/9x - 9x)

To simplify the equation (9x)^-2 = -81x^2, let's begin by writing it in a different form.

First, we can rewrite (9x)^-2 as 1/(9x)^2.

So the equation becomes 1/(9x)^2 = -81x^2.

Next, we can take the reciprocal of both sides of the equation to get rid of the fraction:

(9x)^2/1 = -1/(81x^2)

Since any number divided by 1 remains the same, we can rewrite it as:

(9x)^2 = -1/(81x^2)

Now, let's simplify both sides of the equation.

On the left side, we can square the expression (9x):

81x^2 = -1/(81x^2)

To continue simplifying, let's multiply both sides of the equation by (81x^2):

81x^2 * (81x^2) = -1

Expanding the left side:

6561x^4 = -1

Therefore, the simplified equation is 6561x^4 = -1.