Simplify with steps
(Multiplication and division of fractions)
7x²/2y³ × 3z/5y ÷14xz/10y⁵
To simplify the expression (7x²/2y³) × (3z/5y) ÷ (14xz/10y⁵), we will first simplify each individual fraction and then perform the multiplication and division.
1. 7x²/2y³ can be simplified to 7x² / 2y³ = 7x² / (2y)(y²) = 7x² / (2y)(y)(y) = 7x² / 2y²
2. 3z/5y can be simplified to 3z / 5y = 3z / (5y)
3. 14xz/10y⁵ can be simplified to 14xz / 10y⁵ = 7xz / 5y⁴
Now, the expression becomes: (7x² / 2y²) × (3z / 5y) ÷ (7xz / 5y⁴)
Multiplying the numerators and denominators, we get: (7x² * 3z) / (2y² * 5y) ÷ (7xz / 5y⁴)
Simplifying further, we get: (21xz) / (10y³) ÷ (7xz / 5y⁴)
Re-writing the division as multiplication by the reciprocal, we get: (21xz) / (10y³) * (5y⁴ / 7xz)
Multiplying the numerators and denominators, we get: (21 * 5 * y⁴) / (10 * 7 * y³)
Simplifying, we get: (105y⁴) / (70y³) = 15y
Therefore, the simplified expression is 15y.