Simplify: 8rs^2/5s^4 times (2r^3)^-1
8rS^^2 / 5S^4 * (2r^3)^-1,
8rS^@ / (5S^4*2r^3) =
8rS^@ / 10S^4r^3 = 4rS^2 / 5r^3S^4 =
4r^-2S^-2 / 5 = 4 / 5r^2S^2.
Correction:
8rS^2 / 5S^4*(2r^3)^-1,
8rS^2 / (5S^4*2r^3) =
8rS^3 / 10S^4r^3 = 4rS^2 / 5r^3S^4 =
4r^-2S^-2 / 5 = 4 / 5r^2S^2.
To simplify the expression (8rs^2/5s^4) times (2r^3)^-1, we can start by simplifying the individual terms.
Let's simplify the term 8rs^2/5s^4:
First, we can cancel out the common factors in the numerator and the denominator, which are the 's' terms.
We have:
8rs^2/5s^4 = (8r/5s^2)
Now, let's simplify the term (2r^3)^-1:
The negative exponent indicates that we should take the reciprocal of the term.
So, (2r^3)^-1 = 1/(2r^3)
Now, let's multiply the two simplified terms:
(8r/5s^2) times (1/(2r^3))
To multiply these terms, we multiply the numerators together and multiply the denominators together:
(8r * 1)/(5s^2 * 2r^3) = 8r/(10s^2 * r^3)
Now, let's simplify the expression further. Since we have the same base 'r' in both the numerator and the denominator, we can subtract the exponents:
8r/(10s^2 * r^3) = 8/(10s^2 * r^(3-1))
Simplifying further:
8/10s^2 * r^(2)
Reducing the fraction:
4/5s^2 * r^2
Therefore, the simplified expression is 4/5s^2 * r^2.