Simplify (6x^-2)^2(0.5x)^4.
I have no idea how to do this!, please help!
(6x^-2)^2(0.5x)^4
= (36x^-4)(1/16)(x^4)
= 36/16 x^0 , but x^0 = 1
= 36/16
= 9/4
To simplify the expression (6x^-2)^2(0.5x)^4, we can follow these steps:
Step 1: Simplify the exponents inside the parentheses.
Inside the first set of parentheses, we have x raised to the power of -2. This means we can write (6x^-2)^2 as (6^2)(x^-2)^2. Since x^-2 means 1/x^2, we can rewrite the expression as (6^2)(1/x^2)^2.
Step 2: Simplify the exponents in the second set of parentheses.
Inside the second set of parentheses, we have (1/x^2)^2. When we raise a fraction (like 1/x^2) to a power, we need to raise both the numerator and the denominator to that power. So, (1/x^2)^2 can be written as (1^2)/(x^2)^2, which simplifies to 1/x^4.
Step 3: Combine the numbers outside the parentheses.
Now, we can multiply the numbers outside the parentheses. In this case, (6^2) can be simplified to 36.
Step 4: Simplify the expression by combining like terms.
Finally, we can combine the expression by multiplying the two terms together. Multiply 36 and 1/x^4 to get the final answer:
36 * 1/x^4 = 36/x^4.
So, the simplified form of (6x^-2)^2(0.5x)^4 is 36/x^4.