how do I simplify -2xyz^3/5x^2z^2 times 10xy/x^3
-2xyz^3 / 5x^2z^2 * 10xy / x^3,
-2x^-1yz / 5 * 10x^-2y / 1,
-20x^-3y^2z / 5,
-4y^2z / x^3.
To simplify the expression (-2xyz^3/5x^2z^2) * (10xy/x^3), we can follow these steps:
Step 1: Combine the coefficients.
The coefficient of the first term is -2, and the coefficient of the second term is 10. Multiply these coefficients together: -2 * 10 = -20.
Step 2: Combine the x terms.
In the numerator, we have x * x, which simplifies to x^2. In the denominator, we have x^2 * x, which simplifies to x^3. Since there is an x in both the numerator and denominator, they cancel each other out.
Step 3: Combine the y terms.
In the numerator, we have y * y, which simplifies to y^2. In the denominator, we do not have any y terms, so y does not cancel out.
Step 4: Combine the z terms.
In the numerator, we have z^3 in the first term, and z^2 in the denominator. Since there is one z in the numerator remaining after canceling out z^3 and z^2, we simplify to z.
Putting all the simplifications together, the expression simplifies to:
-20 * y^2 * z / (5 * x)
We can simplify this further:
-20y^2z / 5x
Finally, we can simplify the coefficient and get the simplified expression:
-4y^2z / x