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.