Note: Enter your answer and show all the steps that you use to solve this problem in the space provided. Simplify (6x^-2)^2 (0.5x)^4 show your work
To simplify the expression (6x^-2)^2 (0.5x)^4, we need to apply the exponent rules and perform the necessary calculations. Let's simplify each term separately:
1) Simplifying (6x^-2)^2:
Taking the square of (6x^-2) gives us: (6x^-2)^2 = 6^2 * (x^-2)^2 = 36 * x^(-2 * 2) = 36 * x^-4
2) Simplifying (0.5x)^4:
Taking the fourth power of (0.5x) gives us: (0.5x)^4 = 0.5^4 * (x^1)^4 = 0.0625 * x^4
Now, we can multiply the two simplified terms together:
(36 * x^-4) * (0.0625 * x^4) = 36 * 0.0625 * (x^-4 * x^4) = 2.25 * (x^(-4 + 4)) = 2.25 * x^0
Since any value raised to the 0th power is equal to 1, we have x^0 = 1. Thus, the final simplified expression is:
2.25 * 1 = 2.25
Therefore, the simplified expression of (6x^-2)^2 (0.5x)^4 is 2.25.