# Simplify the expression:

(6ax4)^2(2x)^-2

I will be happy to critique your work or thinking on this.

I will be happy to critique your work or thinking on this.

Note that this is like a fraction with (2x)^2 in the denominator and (6ax^4)^2 in the numerator. You will get some cancellations of powers of x that occur in both numerator and denominator. The ratio of constants that appear in the numerator and denominator (36 and 4) can also be simplified.

## To simplify the expression, let's start by expanding the powers:

(6ax^4)^2 = 6ax^4 * 6ax^4 = 36a^2x^8

(2x)^-2 = 1/(2x)^2 = 1/(2^2 * x^2) = 1/4x^2

Now, let's substitute these expanded expressions back into the original expression:

(6ax^4)^2 * (2x)^-2 = 36a^2x^8 * (1/4x^2)

Next, simplify the expression further:

36a^2x^8 * (1/4x^2)

To simplify this, we can divide the constants and combine the x-terms:

(36/4) * (a^2/x^2) * (x^8/x^2)

This simplifies to:

9a^2 * x^6

So, the simplified expression is 9a^2 * x^6.