To find the quotient of the expression (64y³) / (20y²) / (28y) / (4y), we can start by simplifying the expression step by step.
Step 1: Simplify 64y³ / 20y²
First, we divide the numerical coefficients and the variables separately:
- Numerical part: 64 / 20 simplifies to 16 / 5 by dividing both numerator and denominator by 4.
- Variable part: y³ / y² simplifies to y (subtract the exponents: 3 – 2 = 1).
So, 64y³ / 20y² = (16/5)y.
Step 2: Now divide by 28y
Next, we take the result from Step 1 and divide it by 28y:
- Numerical part: (16 / 5) / 28: This can be rewritten as 16 / (5 * 28) = 16 / 140. This simplifies to 8 / 70, which further simplifies to 4 / 35.
- Variable part: y / y simplifies to 1 (the variable cancels out).
Therefore, ((16/5)y) / (28y) = (4/35).
Step 3: Finally, divide by 4y
Now, we divide the result from Step 2 by 4y:
- Numerical part: (4 / 35) / 4 simplifies to 4 / (35 * 4) = 4 / 140 = 1 / 35.
- Variable part: 1 / y
Putting it all together, we get: ((4 / 35) / (4y)) = (1 / 35y).
Final Answer: Thus, the quotient of 64y³ / 20y² / 28y / 4y is 1 / 35y.