Simplify the expression. (6x^-2)^2(0.5x)^4. Show your work.
I know that the answer is 9x^2-+4
I just need help showing the work.
PLEASE HELP!
Still need help. Please??
anybody?
To simplify the expression (6x^-2)^2(0.5x)^4, follow these steps:
Step 1: Simplify each part of the expression separately.
- Simplify (6x^-2)^2 first:
- Raise 6 to the power of 2: 6^2 = 36
- Apply the exponent of 2 to the variable x^-2: (x^-2)^2 = x^(-2 * 2) = x^-4
- Simplify (0.5x)^4 next:
- Multiply 0.5 by itself four times: (0.5)^4 = 0.5 * 0.5 * 0.5 * 0.5 = 0.0625
- Apply the exponent of 4 to the variable x: x^4
Step 2: Simplify the expression.
Now that we have simplified each part separately, we can combine them:
(6x^-2)^2(0.5x)^4 = (36 * x^-4) * (0.0625 * x^4)
Step 3: Multiply the constants and combine the variables.
Multiply the constants and add the exponents of the variables:
(36 * x^-4) * (0.0625 * x^4) = (36 * 0.0625) * (x^-4 * x^4) = 2.25 * x^0
Step 4: Simplify the expression further.
Any variable raised to the power of 0 is equal to 1, so x^0 = 1:
2.25 * x^0 = 2.25 * 1 = 2.25
Therefore, the simplified expression is 2.25.