Simplify (6x^-2)^2(0.5x)^4 show work please
To simplify the expression (6x^-2)^2(0.5x)^4, we will apply the exponent rules.
First, let's simplify (6x^-2)^2.
When we raise a power to another power, we multiply the exponents. So, (6x^-2)^2 can be written as 6^2 * (x^-2)^2.
6^2 is equal to 36.
To multiply the exponents within the parenthesis, we multiply -2 by 2, which gives us -4.
So, (6x^-2)^2 simplifies to 36 * x^-4 or 36/x^4.
Now, let's simplify (0.5x)^4.
To raise a term with a variable to a power, we multiply the exponents. So, (0.5x)^4 can be written as 0.5^4 * x^4.
0.5^4 is equal to 0.0625.
So, (0.5x)^4 simplifies to 0.0625 * x^4 or 0.0625x^4.
Now, we multiply the simplified expressions together: 36/x^4 * 0.0625x^4.
When we multiply fractions, we multiply the numerators and the denominators separately.
Multiplying the numerators gives us 36 * 0.0625 which is equal to 2.25.
Multiplying the denominators gives us x^4 * x^4 which is equal to x^8.
So, (6x^-2)^2(0.5x)^4 simplifies to 2.25x^8.