simplify (6x^-2)^2(0.5x)^4 show your work

Answer 1

To simplify (6x^-2)^2(0.5x)^4, let's simplify each term separately and then multiply them together.

First, simplify (6x^-2)^2:
(6x^-2)^2 = (6^2)(x^-2)^2 = 36x^(-2*2) = 36x^-4 = 36/x^4

Next, simplify (0.5x)^4:
(0.5x)^4 = (0.5^4)(x^4) = 0.0625x^4

Now, multiply the simplified terms together:
(36/x^4)(0.0625x^4) = (36 * 0.0625)(x^-4 * x^4) = 2.25 * x^(-4+4) = 2.25